Chapter 7.3, Problem 3CYU

To determine

To write the expression in exponential form.

Answer to Problem 3CYU

  ${33}^{\frac{1}{2}}$

Explanation of Solution

Given:

Expression: $\sqrt{33}$

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 $\sqrt{33}$ ,

Applying the formula,

  $\sqrt{33}=\sqrt{{33}^1}$

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

Hence, applying the above formula,

  $\sqrt{{33}^1}={33}^{\frac{1}{2}}$

Conclusion:

Therefore, the exponential form of the expression is ${33}^{\frac{1}{2}}.$