We are asked to evaluate the expression $\sqrt{(-7)^2}$.

ArithmeticExponentsSquare RootsAbsolute ValueOrder of Operations
2025/3/11

1. Problem Description

We are asked to evaluate the expression (7)2\sqrt{(-7)^2}.

2. Solution Steps

First, we evaluate (7)2(-7)^2.
(7)2=(7)×(7)=49(-7)^2 = (-7) \times (-7) = 49
Now, we need to find the square root of
4

9. $\sqrt{49} = 7$

Alternatively, we can use the following property:
x2=x\sqrt{x^2} = |x|
In this case, x=7x = -7.
(7)2=7=7\sqrt{(-7)^2} = |-7| = 7

3. Final Answer

7

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