The sum of a number and 2 is equal to the positive square root of 8 times the number. Find the number.
A)6
B)5
C)2
D)8
E)3

Question

Quizplus · Accepted Answer

Let's start by translating the information given in the problem into an equation:

number + 2 = √(8 x number)

To solve for the number, we'll need to isolate it on one side of the equation.

number + 2 = √(8 x number)

number + 2 = 2√2 x √number (using the fact that √(ab) = √a x √b)

number + 2 = 2√2 x √number

number - 2√2 x √number + 2 = 0

Factor out the common factor of √number:

(√number)(√number - 2√2) + 2 = 0

Now we can solve for √number:

(√number)(√number - 2√2) + 2 = 0

(√number - 2√2)(√number + 1) = 0

The solutions are √number = 2√2 or √number = -1. Since we're looking for a positive number, we can ignore the second solution.

√number = 2√2

Squaring both sides:

number = (2√2)²

number = 8

So the answer is (C) 2.

The Sum of a Number and 2 Is Equal to the Positive