Deck 9: Section 1: Radicals and Rational Exponents

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سؤال
Find the domain of the radical function. <strong>Find the domain of the radical function.  </strong> A)   B) (-∞, ∞) C)   D)   <div style=padding-top: 35px>

A) <strong>Find the domain of the radical function.  </strong> A)   B) (-∞, ∞) C)   D)   <div style=padding-top: 35px>
B) (-∞, ∞)
C) <strong>Find the domain of the radical function.  </strong> A)   B) (-∞, ∞) C)   D)   <div style=padding-top: 35px>
D) <strong>Find the domain of the radical function.  </strong> A)   B) (-∞, ∞) C)   D)   <div style=padding-top: 35px>
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سؤال
Rewrite the expression with a rational denominator. <strong>Rewrite the expression with a rational denominator.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Rewrite the expression with a rational denominator.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Rewrite the expression with a rational denominator.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Rewrite the expression with a rational denominator.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Rewrite the expression with a rational denominator.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Simplify: <strong>Simplify:  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Simplify:  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Simplify:  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Simplify:  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Simplify:  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find the root. Assume the variable represents a positive real number. <strong>Find the root. Assume the variable represents a positive real number.  </strong> A) z<sup>15</sup> B) z<sup>5</sup> C) z<sup>4</sup> D) z <div style=padding-top: 35px>

A) z15
B) z5
C) z4
D) z
سؤال
Find all real solutions. (w - 5)-1/3 = 1

A) {-6, 6}
B) {-24}
C) <strong>Find all real solutions. (w - 5)<sup>-1/3</sup> = 1</strong> A) {-6, 6} B) {-24} C)   D) {6} <div style=padding-top: 35px>
D) {6}
سؤال
Find the root. <strong>Find the root.  </strong> A) -3, 3 B) Not a real number. C) -3 D) 3 <div style=padding-top: 35px>

A) -3, 3
B) Not a real number.
C) -3
D) 3
سؤال
Simplify. Assume the variables represent positive real numbers. <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find all real solutions. (s + 5)2 - 10 = 0

A) <strong>Find all real solutions. (s + 5)<sup>2</sup> - 10 = 0</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find all real solutions. (s + 5)<sup>2</sup> - 10 = 0</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find all real solutions. (s + 5)<sup>2</sup> - 10 = 0</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find all real solutions. (s + 5)<sup>2</sup> - 10 = 0</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Simplify. <strong>Simplify.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Simplify.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Simplify.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Simplify.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Simplify.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate: (125)-4/3

A) <strong>Evaluate: (125)<sup>-4/3</sup></strong> A)   B) 5 C)   D)   <div style=padding-top: 35px>
B) 5
C) <strong>Evaluate: (125)<sup>-4/3</sup></strong> A)   B) 5 C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate: (125)<sup>-4/3</sup></strong> A)   B) 5 C)   D)   <div style=padding-top: 35px>
سؤال
Find all real solutions. <strong>Find all real solutions.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find all real solutions.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find all real solutions.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find all real solutions.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find all real solutions.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Simplify. Assume variables represent positive numbers. <strong>Simplify. Assume variables represent positive numbers.  </strong> A) The expression cannot be simplified. B)   C)   D)   <div style=padding-top: 35px>

A) The expression cannot be simplified.
B)
<strong>Simplify. Assume variables represent positive numbers.  </strong> A) The expression cannot be simplified. B)   C)   D)   <div style=padding-top: 35px>
C)
<strong>Simplify. Assume variables represent positive numbers.  </strong> A) The expression cannot be simplified. B)   C)   D)   <div style=padding-top: 35px>
D)
<strong>Simplify. Assume variables represent positive numbers.  </strong> A) The expression cannot be simplified. B)   C)   D)   <div style=padding-top: 35px>
سؤال
Simplify. <strong>Simplify.  </strong> A) The expression cannot be rationalized. B)   C)   D)   <div style=padding-top: 35px>

A) The expression cannot be rationalized.
B)
<strong>Simplify.  </strong> A) The expression cannot be rationalized. B)   C)   D)   <div style=padding-top: 35px>
C)
<strong>Simplify.  </strong> A) The expression cannot be rationalized. B)   C)   D)   <div style=padding-top: 35px>
D)
<strong>Simplify.  </strong> A) The expression cannot be rationalized. B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find all real solutions. <strong>Find all real solutions.  </strong> A) {1, 2} B) {-1, 1} C)   D) {-1} <div style=padding-top: 35px>

A) {1, 2}
B) {-1, 1}
C) <strong>Find all real solutions.  </strong> A) {1, 2} B) {-1, 1} C)   D) {-1} <div style=padding-top: 35px>
D) {-1}
سؤال
Write in simplified radical form. <strong>Write in simplified radical form.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Write in simplified radical form.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Write in simplified radical form.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Write in simplified radical form.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Write in simplified radical form.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find the product. <strong>Find the product.  </strong> A) -21 B) 89 C) 111 D) 1 <div style=padding-top: 35px>

A) -21
B) 89
C) 111
D) 1
سؤال
Simplify. Assume the variables represent positive real numbers. <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Simplify: 812/3 ÷\div 811/6

A) 9
B)  <strong>Simplify: 81<sup>2/3</sup>  \div  81<sup>1/6</sup></strong> A) 9 B)   C)   D) 81 <div style=padding-top: 35px>
C)  <strong>Simplify: 81<sup>2/3</sup>  \div  81<sup>1/6</sup></strong> A) 9 B)   C)   D) 81 <div style=padding-top: 35px>
D) 81
سؤال
Find all real solutions. -7(x - 5)9 = 0

A) {0}
B) <strong>Find all real solutions. -7(x - 5)<sup>9</sup> = 0</strong> A) {0} B)   C) {5} D) {-5, 5} <div style=padding-top: 35px>
C) {5}
D) {-5, 5}
سؤال
Simplify. <strong>Simplify.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Simplify.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Simplify.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Simplify.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Simplify.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find the complex solutions. <strong>Find the complex solutions.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the complex solutions.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the complex solutions.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the complex solutions.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the complex solutions.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find the quotient. <strong>Find the quotient.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the quotient.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the quotient.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the quotient.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the quotient.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Write the expression in the form a + bi, where a and b are real numbers. <strong>Write the expression in the form a + bi, where a and b are real numbers.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Write the expression in the form a + bi, where a and b are real numbers.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Write the expression in the form a + bi, where a and b are real numbers.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Write the expression in the form a + bi, where a and b are real numbers.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Write the expression in the form a + bi, where a and b are real numbers.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find the difference. (1 + 4i) - (-7 + 7i)

A) -6 - 3i
B) 8 + 11i
C) -6 + 11i
D) 8 - 3i
سؤال
The diagonal of a square measures 12 inches. What is the length of the sides?

A) 6 <strong>The diagonal of a square measures 12 inches. What is the length of the sides?</strong> A) 6   inches B) 6   inches C) 12   inches D) 6 inches <div style=padding-top: 35px> inches
B) 6 <strong>The diagonal of a square measures 12 inches. What is the length of the sides?</strong> A) 6   inches B) 6   inches C) 12   inches D) 6 inches <div style=padding-top: 35px> inches
C) 12 <strong>The diagonal of a square measures 12 inches. What is the length of the sides?</strong> A) 6   inches B) 6   inches C) 12   inches D) 6 inches <div style=padding-top: 35px> inches
D) 6 inches
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Deck 9: Section 1: Radicals and Rational Exponents
1
Find the domain of the radical function. <strong>Find the domain of the radical function.  </strong> A)   B) (-∞, ∞) C)   D)

A) <strong>Find the domain of the radical function.  </strong> A)   B) (-∞, ∞) C)   D)
B) (-∞, ∞)
C) <strong>Find the domain of the radical function.  </strong> A)   B) (-∞, ∞) C)   D)
D) <strong>Find the domain of the radical function.  </strong> A)   B) (-∞, ∞) C)   D)
2
Rewrite the expression with a rational denominator. <strong>Rewrite the expression with a rational denominator.  </strong> A)   B)   C)   D)

A) <strong>Rewrite the expression with a rational denominator.  </strong> A)   B)   C)   D)
B) <strong>Rewrite the expression with a rational denominator.  </strong> A)   B)   C)   D)
C) <strong>Rewrite the expression with a rational denominator.  </strong> A)   B)   C)   D)
D) <strong>Rewrite the expression with a rational denominator.  </strong> A)   B)   C)   D)
3
Simplify: <strong>Simplify:  </strong> A)   B)   C)   D)

A) <strong>Simplify:  </strong> A)   B)   C)   D)
B) <strong>Simplify:  </strong> A)   B)   C)   D)
C) <strong>Simplify:  </strong> A)   B)   C)   D)
D) <strong>Simplify:  </strong> A)   B)   C)   D)
4
Find the root. Assume the variable represents a positive real number. <strong>Find the root. Assume the variable represents a positive real number.  </strong> A) z<sup>15</sup> B) z<sup>5</sup> C) z<sup>4</sup> D) z

A) z15
B) z5
C) z4
D) z
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5
Find all real solutions. (w - 5)-1/3 = 1

A) {-6, 6}
B) {-24}
C) <strong>Find all real solutions. (w - 5)<sup>-1/3</sup> = 1</strong> A) {-6, 6} B) {-24} C)   D) {6}
D) {6}
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6
Find the root. <strong>Find the root.  </strong> A) -3, 3 B) Not a real number. C) -3 D) 3

A) -3, 3
B) Not a real number.
C) -3
D) 3
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7
Simplify. Assume the variables represent positive real numbers. <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)

A) <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)
B) <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)
C) <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)
D) <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)
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8
Find all real solutions. (s + 5)2 - 10 = 0

A) <strong>Find all real solutions. (s + 5)<sup>2</sup> - 10 = 0</strong> A)   B)   C)   D)
B) <strong>Find all real solutions. (s + 5)<sup>2</sup> - 10 = 0</strong> A)   B)   C)   D)
C) <strong>Find all real solutions. (s + 5)<sup>2</sup> - 10 = 0</strong> A)   B)   C)   D)
D) <strong>Find all real solutions. (s + 5)<sup>2</sup> - 10 = 0</strong> A)   B)   C)   D)
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9
Simplify. <strong>Simplify.  </strong> A)   B)   C)   D)

A) <strong>Simplify.  </strong> A)   B)   C)   D)
B) <strong>Simplify.  </strong> A)   B)   C)   D)
C) <strong>Simplify.  </strong> A)   B)   C)   D)
D) <strong>Simplify.  </strong> A)   B)   C)   D)
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10
Evaluate: (125)-4/3

A) <strong>Evaluate: (125)<sup>-4/3</sup></strong> A)   B) 5 C)   D)
B) 5
C) <strong>Evaluate: (125)<sup>-4/3</sup></strong> A)   B) 5 C)   D)
D) <strong>Evaluate: (125)<sup>-4/3</sup></strong> A)   B) 5 C)   D)
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11
Find all real solutions. <strong>Find all real solutions.  </strong> A)   B)   C)   D)

A) <strong>Find all real solutions.  </strong> A)   B)   C)   D)
B) <strong>Find all real solutions.  </strong> A)   B)   C)   D)
C) <strong>Find all real solutions.  </strong> A)   B)   C)   D)
D) <strong>Find all real solutions.  </strong> A)   B)   C)   D)
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12
Simplify. Assume variables represent positive numbers. <strong>Simplify. Assume variables represent positive numbers.  </strong> A) The expression cannot be simplified. B)   C)   D)

A) The expression cannot be simplified.
B)
<strong>Simplify. Assume variables represent positive numbers.  </strong> A) The expression cannot be simplified. B)   C)   D)
C)
<strong>Simplify. Assume variables represent positive numbers.  </strong> A) The expression cannot be simplified. B)   C)   D)
D)
<strong>Simplify. Assume variables represent positive numbers.  </strong> A) The expression cannot be simplified. B)   C)   D)
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13
Simplify. <strong>Simplify.  </strong> A) The expression cannot be rationalized. B)   C)   D)

A) The expression cannot be rationalized.
B)
<strong>Simplify.  </strong> A) The expression cannot be rationalized. B)   C)   D)
C)
<strong>Simplify.  </strong> A) The expression cannot be rationalized. B)   C)   D)
D)
<strong>Simplify.  </strong> A) The expression cannot be rationalized. B)   C)   D)
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14
Find all real solutions. <strong>Find all real solutions.  </strong> A) {1, 2} B) {-1, 1} C)   D) {-1}

A) {1, 2}
B) {-1, 1}
C) <strong>Find all real solutions.  </strong> A) {1, 2} B) {-1, 1} C)   D) {-1}
D) {-1}
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15
Write in simplified radical form. <strong>Write in simplified radical form.  </strong> A)   B)   C)   D)

A) <strong>Write in simplified radical form.  </strong> A)   B)   C)   D)
B) <strong>Write in simplified radical form.  </strong> A)   B)   C)   D)
C) <strong>Write in simplified radical form.  </strong> A)   B)   C)   D)
D) <strong>Write in simplified radical form.  </strong> A)   B)   C)   D)
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16
Find the product. <strong>Find the product.  </strong> A) -21 B) 89 C) 111 D) 1

A) -21
B) 89
C) 111
D) 1
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17
Simplify. Assume the variables represent positive real numbers. <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)

A) <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)
B) <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)
C) <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)
D) <strong>Simplify. Assume the variables represent positive real numbers.  </strong> A)   B)   C)   D)
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18
Simplify: 812/3 ÷\div 811/6

A) 9
B)  <strong>Simplify: 81<sup>2/3</sup>  \div  81<sup>1/6</sup></strong> A) 9 B)   C)   D) 81
C)  <strong>Simplify: 81<sup>2/3</sup>  \div  81<sup>1/6</sup></strong> A) 9 B)   C)   D) 81
D) 81
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19
Find all real solutions. -7(x - 5)9 = 0

A) {0}
B) <strong>Find all real solutions. -7(x - 5)<sup>9</sup> = 0</strong> A) {0} B)   C) {5} D) {-5, 5}
C) {5}
D) {-5, 5}
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20
Simplify. <strong>Simplify.  </strong> A)   B)   C)   D)

A) <strong>Simplify.  </strong> A)   B)   C)   D)
B) <strong>Simplify.  </strong> A)   B)   C)   D)
C) <strong>Simplify.  </strong> A)   B)   C)   D)
D) <strong>Simplify.  </strong> A)   B)   C)   D)
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21
Find the complex solutions. <strong>Find the complex solutions.  </strong> A)   B)   C)   D)

A) <strong>Find the complex solutions.  </strong> A)   B)   C)   D)
B) <strong>Find the complex solutions.  </strong> A)   B)   C)   D)
C) <strong>Find the complex solutions.  </strong> A)   B)   C)   D)
D) <strong>Find the complex solutions.  </strong> A)   B)   C)   D)
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22
Find the quotient. <strong>Find the quotient.  </strong> A)   B)   C)   D)

A) <strong>Find the quotient.  </strong> A)   B)   C)   D)
B) <strong>Find the quotient.  </strong> A)   B)   C)   D)
C) <strong>Find the quotient.  </strong> A)   B)   C)   D)
D) <strong>Find the quotient.  </strong> A)   B)   C)   D)
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23
Write the expression in the form a + bi, where a and b are real numbers. <strong>Write the expression in the form a + bi, where a and b are real numbers.  </strong> A)   B)   C)   D)

A) <strong>Write the expression in the form a + bi, where a and b are real numbers.  </strong> A)   B)   C)   D)
B) <strong>Write the expression in the form a + bi, where a and b are real numbers.  </strong> A)   B)   C)   D)
C) <strong>Write the expression in the form a + bi, where a and b are real numbers.  </strong> A)   B)   C)   D)
D) <strong>Write the expression in the form a + bi, where a and b are real numbers.  </strong> A)   B)   C)   D)
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24
Find the difference. (1 + 4i) - (-7 + 7i)

A) -6 - 3i
B) 8 + 11i
C) -6 + 11i
D) 8 - 3i
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25
The diagonal of a square measures 12 inches. What is the length of the sides?

A) 6 <strong>The diagonal of a square measures 12 inches. What is the length of the sides?</strong> A) 6   inches B) 6   inches C) 12   inches D) 6 inches inches
B) 6 <strong>The diagonal of a square measures 12 inches. What is the length of the sides?</strong> A) 6   inches B) 6   inches C) 12   inches D) 6 inches inches
C) 12 <strong>The diagonal of a square measures 12 inches. What is the length of the sides?</strong> A) 6   inches B) 6   inches C) 12   inches D) 6 inches inches
D) 6 inches
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