Chapter SH, Problem 6.11EP

To determine

Find the simplified form of the given expression.

Answer to Problem 6.11EP

The simplified form of the expression is $6a{b}^2$ .

Explanation of Solution

Given:

The given expression is $\sqrt{36a^2{b}^4}$ .

Calculation:

  $\sqrt{36a^2{b}^4}$

Use exponent rule $x^{pq}={\left(x^p\right)}^q$ .

  $\begin{array}{l}\sqrt{36a^2{b}^4}\\ =\sqrt{6^2{a}^2{\left(b^2\right)}^2}\\ =\sqrt{6^2}\sqrt{a^2}\sqrt{{\left(b^2\right)}^2}\end{array}$

Apply radical property $\sqrt[n]{x^n}=x,x\ge 0$ .

  $=6a{b}^2$

Hence the simplified form of the expression is $6a{b}^2$ .