Chapter 9.1, Problem 13PSC

a.

To determine

To simplify the given expression. Value of $h$

Answer to Problem 13PSC

The simplification value of expression is $h$ and $-h$ .

Explanation of Solution

Given: “ $h$ ” represents a negative number.

Calculation: Here, $h<0$ (given)

Therefore,

  $\begin{array}{l}=\sqrt{{\left(h\right)}^2}\\ =\sqrt{h^2}\text{ [because square makes the value positive]}\\ \text{=}\pm h\end{array}$

Conclusion: Hence, the simplification value of expression $\pm h$ .

b.

To determine

To Simplify:The $\sqrt{{(x-3)}^2}$ when the $x$ is less than 3.

Answer to Problem 13PSC

The Simplification value of expression is $\pm (x-3)$

Explanation of Solution

Given: “ x ” is less than $3$

Calculation: The expression is given as follows

  $=\sqrt{{\left(x-3\right)}^2}$

If “ x ” is less than 3, then the value of the $(x-3)$ would b negative. But due to square it becomes positive.

Therefore, on simplification it would be

  $=\pm (x-3)$

c.

To determine

To find: The Simplified value of the equation $\sqrt{p^2{q}^2}$

Answer to Problem 13PSC

The simplified value of the equation $\sqrt{p^2{q}^2}$ is $pq$

Explanation of Solution

Given: “ p ” and “ q ” both represents negative numbers.

Calculation: Here, $p<0,q<0$

If we square any number of them it will become positive.

So, the required value will be $pq$

Conclusion: Hence, the simplified value of the equation $\sqrt{p^2{q}^2}$ is $pq$

d.

To determine

To find: Thesimplified value of the equation $\sqrt{x^3{y}^2}$

Answer to Problem 13PSC

Simplified value of the expression is $xy\sqrt{x}$

Explanation of Solution

Given: “ x ” is greater than $0$ and “ y ” is less than $0$

Calculation: Here, $x>0,y<0$

Here, “ x ” is always positive and “ y ” becomes positive when it will square.

So, the required value will be $xy\sqrt{x}$

Conclusion: Hence, the simplified value of the equation $\sqrt{x^3{y}^2}$ is $xy\sqrt{x}$