Chapter A.10, Problem 2AYU

To determine

To find: The value of $\sqrt{16}$ and $\sqrt{{\left(-4\right)}^2}$.

Answer to Problem 2AYU

The value of $\sqrt{16}=4$ and $\sqrt{{\left(-4\right)}^2}=4$.

Explanation of Solution

Given:

It is asked to find the value of $\sqrt{16}$ and $\sqrt{{\left(-4\right)}^2}$.

Formula used:

If $n\ge 2$ is an integer and $a$ is a real number, then

$\sqrt[n]{a^n}=a$ if $n\ge 3$ is odd.

$\sqrt[n]{a^n}=\left|a\right|$ if $n\ge 2$ is even.

Calculation:

Consider $\sqrt{16}= \sqrt{4^2}=\left|4\right|=4$.

Consider $\sqrt{{\left(-4\right)}^2}=\left|-4\right|=4$.