Chapter 7.3, Problem 20PPS

To determine

To write the expression in radical form.

Answer to Problem 20PPS

  $2\sqrt{3y}$

Explanation of Solution

Given:

Expression: ${(12y)}^{\frac{1}{2}}$

Formula used:

A relationship between radical and exponential is:

  $x^{\frac{a}{b}}=\sqrt[b]{x^a}$

Here, $x^{\frac{a}{b}}$ is an exponential whereas $\sqrt[b]{x^a}$ is a radical.

Calculation:

Consider the given expression ${(12y)}^{\frac{1}{2}}$ ,

The above expression is of the form $x^{\frac{a}{b}}.$

Applying the above formula,

  $\begin{array}{c}$ {(12y)}^{\frac{1}{2}}$=\sqrt{12y^1}\\ =\sqrt{4\times 3y}\\ =2\sqrt{3y}\end{array}$

Conclusion:

Therefore, the radical form of the expression is $2\sqrt{3y}.$