Chapter 8, Problem 481RE

In the following exercises, simplify.

481.

a. $\sqrt{225}$

b. $-\sqrt{16}$

To determine

(a)

The simplification of roots from the given expression.

Answer to Problem 481RE

$15$

Explanation of Solution

Given information:- A number is given as $\sqrt{225}$.

Calculations:-

When a given number is a perfect square, we find its square root as shown below:

$\begin{array}{l}\Rightarrow 225=3\times 3\times 5\times 5\text{ [Evaluate the given number into prime factor]}\\ \Rightarrow 225=\underset{\_}{3\times 3}\times \underset{\_}{5\times 5}\text{ [Make pair of similar factor]}\\ \Rightarrow \sqrt{225}\text{=3}\times 5\text{ [Take one factor out of each pair]}\\ \Rightarrow \sqrt{225}=15{\text{ [where,15}}^2\text{=225]}\end{array}$

Thus, $\sqrt{225}$ is a perfect square.

Hence, $15$ is the number whose square is $225$.

To determine

(b)

The simplification of roots from the given expression.

Answer to Problem 481RE

$-4$

Explanation of Solution

Given information:- A number is given as $-\sqrt{16}$.

Calculations:-

When a given number is a perfect square, we find its square root as shown below:

$\begin{array}{l}\Rightarrow 16=2\times 2\times 2\times 2\text{ [Evaluate the given number into prime factor]}\\ \Rightarrow 16=\underset{\_}{2\times 2}\times \underset{\_}{2\times 2}\text{ [Make pair of similar factor]}\\ \Rightarrow \sqrt{16}\text{=2}\times 2\text{ [Take one factor out of each pair]}\\ \Rightarrow \sqrt{16}=4{\text{ [where,4}}^2\text{=16]}\\ \text{If we want the negative square root of the given number,then you must be use a negative }\\ \text{sign (outside of the square root)}\text{.}\\ \therefore -\sqrt{16}=-4\end{array}$

Thus, $-\sqrt{16}$ is a perfect square.

Hence, $-4$ is the number whose square is $16$.