# To calculate: The single radical of the expression \sqrt{5}\cdot\sqrt[3]

Joni Kenny 2021-11-06 Answered

To calculate: The single radical of the expression
$\sqrt{5}\cdot \sqrt[3]{4}$

You can still ask an expert for help

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

irwchh

Step 1
The formula:
a) $\sqrt[n]{ab}=\sqrt[n]{a}\cdot \sqrt[n]{b}$
b) $\sqrt[n]{a}={a}^{1/n}$
Step 2
a) $\sqrt{5}\cdot \sqrt[3]{4}=\left(5{\right)}^{\frac{1}{2}×\frac{3}{3}}\cdot \left(4{\right)}^{\frac{1}{3}×\frac{2}{2}}$
$={\left(5\right)}^{\frac{3}{6}}\cdot {\left(4\right)}^{\frac{2}{6}}$
$=\sqrt[6]{{5}^{3}}\cdot \sqrt[6]{{4}^{2}}$
b) $\sqrt{5}\cdot \sqrt[3]{4}=\sqrt[6]{\left(5{\right)}^{3}\left(4{\right)}^{2}}$
$=\sqrt[6]{125\cdot 16}$
$=\sqrt[6]{2000}$