Q. 8.51 - Intermediate Algebra

Question

Write as a radical expression:

(a) $t^{\frac{1}{2}}$

(b) $m^{\frac{1}{3}}$

(c) $r^{\frac{1}{4}}$

Step-by-Step Solution

Answer

The radical expression of $t^{\frac{1}{2}}$ is $\sqrt{t}$.

The radical expression of $m^{\frac{1}{3}}$ is $\sqrt[3]{m}$.

The radical expression of $r^{\frac{1}{4}}$ is $\sqrt[4]{r}$.

Part (a) Step 1. Given

The expression $t^{\frac{1}{2}}$

To write the given expression in the form of $\sqrt[n]{a}$

Part (a) Step 2. Write as rational expression

The denominator of rational exponent is $2$, so the index of the radical is $2$.

We do not show the index when the index is $2$.

The radical expression is $\sqrt{t}$

Part (b) Step 1. Given

The expression $m^{\frac{1}{3}}$

To write the given expression in the form of $\sqrt[n]{a}$

Part (b) Step 2. Write as rational expression

The denominator of the exponent is $3$, so the index is $3$.

The radical expression is $\sqrt[3]{m}$

Part (c) Step 1. Given

The expression $r^{\frac{1}{4}}$

To write the given expression in the form of $\sqrt[n]{a}$

Part (c) Step 2. Write as rational expression

The denominator of the exponent is $4$, so the index is $4$.

The radical expression is $\sqrt[4]{r}$