Problem 12 - College Algebra

Question

Evaluate each expression or indicate that the root is not a real number. $$\sqrt{(-17)^{2}}$$

Step-by-Step Solution

Answer

The value of the expression \(\sqrt{(-17)^{2}}\) is 17.

Step 1: Identify the given expression

The given expression to evaluate is \(\sqrt{(-17)^{2}}\).

Step 2: Evaluate the base

Evaluate the expression inside the square root first, which is \((-17)^{2}\). The product of two negative numbers is positive, so \((-17)^{2} = 289\).

Step 3: Simplify the square root

Evaluate \(\sqrt{289}\). The square root of 289 is 17, because \(17 \times 17 = 289\).