Chapter EP, Problem 7.4.21EP

To determine

To calculate: The simplified form of the expression $\pm \sqrt{16m^6{p}^2}$ .

Answer to Problem 7.4.21EP

The simplified form of the expression $\pm \sqrt{16m^6{p}^2}$ is $\pm 4m^{3}p$ .

Explanation of Solution

Given information:

The expression $\pm \sqrt{16m^6{p}^2}$ .

Formula used:

If a andb are real numbers and n is a positive integer if $a^n=b$ then a is an nth root of b .

Calculation:

Consider the expression $\pm \sqrt{16m^6{p}^2}$ .

Recall that if a andb are real numbers and n is a positive integer if $a^n=b$ then a is an nth root of b .

Rewrite the expression as,

  $\begin{array}{c}\pm \sqrt{16m^6{p}^2}=\pm {\left(16m^6{p}^2\right)}^{\frac{1}{2}}\\ =\pm 4m^{3}p\end{array}$

Square root of $16m^6{p}^2$ is $\pm 4m^{3}p$ .

Thus, the simplified form of the expression $\pm \sqrt{16m^6{p}^2}$ is $\pm 4m^{3}p$ .