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Which number, when placed in the box, will make the equation true?

◻^(2)=sqrt64
A.
sqrt8
B.
sqrt32
C. 16
D. 32

Which number, when placed in the box, will make the equation true? $\newline$ $\square^{2}=\sqrt{64}$ $\newline$ A. $\sqrt{8}$ $\newline$ B. $\sqrt{32}$ $\newline$ C. $16$ $\newline$ D. $32$

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Simplify radical expressions with variables II

Full solution

Q. Which number, when placed in the box, will make the equation true?

\newline

\square^{2}=\sqrt{64}

\newline

A.

\sqrt{8}

\newline

B.

\sqrt{32}

\newline

C.

16

\newline

D.

32

Simplify square root of $64$ : We need to find a number that, when squared, equals the square root of $64$ . Let's first simplify the square root of $64$ . $\newline$ $\sqrt{64} = 8$ , because $8 \times 8 = 64$ .
Find square root of $8$ : Now we need to find a number that, when squared, equals $8$ . This means we are looking for the square root of $8$ , because $(\sqrt{8})^2 = 8$ .
Check given options: Let's check the options given to see which one, when squared, equals $8$ . $\newline$ Option A is $\sqrt{8}$ , which when squared, gives us $8$ . $\newline$ Option B is $\sqrt{32}$ , which when squared, gives us $32$ . $\newline$ Option C is $16$ , which when squared, gives us $256$ . $\newline$ Option D is $32$ , which when squared, gives us $1024$ .
Identify correct answer: From the above step, we can see that only Option A, when squared, equals $8$ . Therefore, Option A is the correct answer.

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