Question 1

Divide rationalize the denominator and simplify. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Divide rationalize the denominator and simplify. 
A)...

Question 2

To rationalize the denominator means to get rid of radical expressions in the numerator.

Accepted Answer

To rationalize the denominator means to get rid of radical expressions in the denominator, not the numerator.

Question 3

The distributive property  applies to radical expressions.

Accepted Answer

The answer of The distributive property  applies to radical...

Question 4

Multiply the radicals and simplify. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Multiply the radicals and simplify. 
A) 
B)...

Question 5

The quotient property of radicals states that for  and   .

Accepted Answer

This statement is true. The quotient property of radicals states that the division of two radicals with the same index is equal to the radical of the quotient of their radicands. In other words, the square root of a divided by the square root of b is equal to the square root of (a/b).

Question 6

Multiply the radicals and simplify. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Multiply the radicals and simplify. 
A) 
B)...

Question 7

The area of the rectangle below is  . Its width is  . Find its length. 
A) 15.5
B) 1.5
C) 
D)

Accepted Answer

The answer of The area of the rectangle below is...

Question 8

Multiply the radicals and simplify. 
A) 
B) 
C) 
D)

Accepted Answer

To multiply radicals, we multiply the coefficients and then multiply the radicands. In this case, 11 times 9 is 99 and e^2 times e^3 is e^5. Therefore, the simplified answer is 99e^5, which matches the radicand in choice C.

Question 9

Multiply the radicals and simplify. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Multiply the radicals and simplify. 
A) 
B)...

Question 10

When you multiply a radical expression with two terms by its conjugate the result has no more radicals in its simplified form.

Accepted Answer

When you multiply a radical expression with two terms by its conjugate, you get a difference of squares in the result which eliminates the radical. This is because when you multiply the two conjugates, the middle terms cancel out and you are left with the square of the first term minus the square of the second term. This result can be simplified further, but it will not contain any radicals.

Question 11

Multiply the radicals and simplify. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Multiply the radicals and simplify. 
A) 
B)...

Question 12

Multiply the radicals and simplify. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Multiply the radicals and simplify. 
A) 
B)...

Question 13

Divide and simplify. 
A) 
B) 
C) 
D)

Accepted Answer

Without knowing what the symbols represent, it is impossible to perform any division or simplification. The answer is simply the given expression. Therefore, the correct answer is C, which matches the given expression.

Question 14

Multiply the radicals and simplify. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Multiply the radicals and simplify. 
A) 
B)...

Question 15

Multiply the radicals and simplify. 
A) 
B) 
C) 
D)

Accepted Answer

When multiplying radicals, you can simplify by multiplying the constants and multiplying the coefficients (or the numbers in front of the radicals) together. Then, you can multiply the radicands (or the numbers inside the radicals) together.

In this case, the constants are the same (11ec19db_851f_f946_9dbe_7505bccb97a8_TBX8673_11), so we only need to focus on multiplying the coefficients and radicands.

The first radical has a coefficient of 11 and a radicand of ec19db_851f_f946_9dbe_7505bccb97a8_TBX8673_11. The second radical has a coefficient of 11 and a radicand of db. Multiplying the coefficients gives us 11*11 = 121. Multiplying the radicands gives us ec19db_851f_f946_9dbe_7505bccb97a8_TBX8673_11 * db, which simplifies to ec19db_851f_f947_9dbe_cbefe0070ca3_TBX8673_11.

Putting this together, we get 121ec19db_851f_f947_9dbe_cbefe0070ca3_TBX8673_11, which matches option D.

Question 16

Multiply the radicals and simplify. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Multiply the radicals and simplify. 
A) 
B)...

Question 17

Multiply the radicals and simplify. 
A) 
B) 
C) 
D)

Accepted Answer

To simplify the expression, we need to multiply the numbers outside the radical and then multiply the numbers inside the radical.

$3\sqrt{11} \cdot 7\sqrt{17} = 21\sqrt{187}$

The result can't be simplified further, so the correct answer is B.

Question 18

The conjugate of  is  .

Accepted Answer

The answer of The conjugate of  is  ....

Question 19

Rationalize the denominator and simplify. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Rationalize the denominator and simplify. 
A) 
B)...

Question 20

Find the area of the isosceles right triangle. The length of its legs is  . 
A) 
B) 208
C) 104
D)

Accepted Answer

The answer of Find the area of the isosceles right...

Quiz 8: Radical Expressions and Equations

Divide rationalize the denominator and simplify.

To rationalize the denominator means to get rid of radical expressions in the numerator.

The distributive property applies to radical expressions.

Multiply the radicals and simplify.

The quotient property of radicals states that for and .

Multiply the radicals and simplify.

The area of the rectangle below is . Its width is . Find its length.

Multiply the radicals and simplify.

Multiply the radicals and simplify.

When you multiply a radical expression with two terms by its conjugate the result has no more radicals in its simplified form.

Multiply the radicals and simplify.

Multiply the radicals and simplify.

Divide and simplify.

Multiply the radicals and simplify.

Multiply the radicals and simplify.

Multiply the radicals and simplify.

Multiply the radicals and simplify.

The conjugate of is .

Rationalize the denominator and simplify.

Find the area of the isosceles right triangle. The length of its legs is .