Chapter A.1, Problem 56E

Solution

Write using a single radical.

  $a^{\frac{7}{6}}$ .

Given:

The given expression is $\sqrt{a}\sqrt[3]{a^2}$ .

Concept Used:

• Radical - The v symbol that is used to denote square root or nth roots.

Calculation:

The given expression is $\sqrt{a}\sqrt[3]{a^2}$ .

  $\begin{array}{c}$ \sqrt{a}\sqrt[3]{a^2}={(a)}^{1/2}{(a^2)}^{1/3}$$ ={(a)}^{1/2}(a^{2\cdot \frac{1}{3}})$$ ={(a)}^{1/2}(a^{2/3})$=a^{\frac{1}{2}+\frac{2}{3}}\\ =a^{\frac{3+4}{6}}\\ =a^{\frac{7}{6}}\end{array}$

Thus the single radical expression of $\sqrt{a}\sqrt[3]{a^2}$ is $a^{\frac{7}{6}}$ .