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Chapter 0: Problem 54

Evaluate the expressions, rounding your answer to four significant digits where necessary. $$ \sqrt{(-1)^{2}} $$

Short Answer

Expert verified
To evaluate the expression, first simplify the exponent: \((-1)^2 = 1\). Next, evaluate the square root: \(\sqrt{1} = 1\). Thus, \(\sqrt{(-1)^{2}} = 1\).

Step by step solution

01

Simplify the exponent

First, we need to simplify the exponent $$(-1)^2$$. Remember that any non-zero number raised to the power of 2 is equal to the square of that number: $$ (-1)^2 = (-1) \times (-1) = 1 $$
02

Evaluate the square root

Now that we have simplified the exponent, we can evaluate the square root of the result: $$ \sqrt{1} = 1 $$ Since the result is an integer, there's no need to round it to four significant digits. The evaluation of the expression is complete, and the final answer is: $$ \sqrt{(-1)^{2}} = 1 $$

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