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Chapter 8: Problem 92

What are the square roots of \(36 ?\) Explain why each of these numbers is a square root.

Short Answer

Expert verified
The square roots of 36 are 6 and -6. These numbers are square roots of 36 because when they are squared, the result is 36.

Step by step solution

01

Identify the task

The task here is to identify the square roots of 36. Square roots of a number \(x\) are numbers that, when squared, give \(x\) as the result.
02

Compute positive square root

Start by taking the positive square root. \(\sqrt{36}=6\) because \(6^2=36\). So, 6 is a square root of 36.
03

Compute negative square root

Now, take the negative square root. \(-\sqrt{36}=-6\) because \((-6)^2=36\). So, -6 is also a square root of 36.
04

Explain why these numbers are square roots

These numbers are square roots of 36 because when they are squared, the result is 36. This is inline with the definition of square roots that says 'A number that when squared gives the original number'.

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$-3^{-2}=\frac{1}{9}$$

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