Problem 11 - College Algebra

Question

Evaluate each expression or indicate that the root is not a real number. $$\sqrt{(-13)^{2}}$$

Step-by-Step Solution

Answer

The value of the given expression \(\sqrt{(-13)^{2}}\) is 13.

Step 1: Squaring the number

First, square the number -13. This is done by multiplying -13 by -13 which gives the result 169. So, \((-13)^{2}=169\).

Step 2: Taking the square root

Next, take the square root of 169. The square root of a number is a value that, when multiplied by itself, gives the original number. Here, \(\sqrt{169} = 13\).

Step 3: Evaluating the expression

Finally, replace the sum into the original expression. So, \(\sqrt{(-13)^{2}} = \sqrt{169} = 13\).