Chapter 7, Problem 1RE

To determine

To calculate: The value of expression $\sqrt{9}$.

Answer to Problem 1RE

Solution:

The value of expression $\sqrt{9}$ is $3$.

Explanation of Solution

Given Information:

The provided expression is $\sqrt{9}$.

Formula used:

Root of a nonnegative real number is nonnegative,

that is $\sqrt[n]{a}=b$ where $a,b$ both are nonnegative real numbers.

For a given real number x, square root of $x^2$ is the absolute value of x, that is:

$\sqrt{x^2}=\left|x\right|$

Calculation:

Consider the radical expression $\sqrt{9}$,

Rewrite the expression as,

$\begin{array}{c}\sqrt{9}=\sqrt{3\times 3}\\ =\sqrt{3^2}\\ =\left|3\right|\end{array}$

As $3$ is a real number, $\left|3\right|=3$.

Thus, the radical expression $\sqrt{9}$ evaluates to 3.