# To calculate: \sqrt{\frac{3y}{20}} The single radical of the expression.

To calculate: $\sqrt{\frac{3y}{20}}$
The single radical of the expression.
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Aamina Herring

Formula:
$\sqrt[n]{a}={a}^{1/n}$
$\left(\sqrt[n]{a}{\right)}^{m}=\sqrt[n]{{a}^{m}}$
$={a}^{\frac{m}{n}}$
The product rule for radicals is:
a) $\sqrt[n]{ab}=\sqrt[n]{a}\cdot \sqrt[n]{b}$
The quotient rule for radicals is:
b) $\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$
Calculation:
a) $\sqrt{\frac{3y}{20}}=\sqrt{\frac{3y}{5\cdot 4}}$
$=\sqrt{\frac{3y}{5\cdot {2}^{2}}}$
$=\frac{1}{2}\sqrt{\frac{3y}{5}}$
b) $\sqrt{\frac{3y}{20}}=\frac{1}{2}\sqrt{\frac{3y}{5}}×\frac{\sqrt{5}}{\sqrt{5}}$
$=\frac{1}{2}\frac{\sqrt{3}\cdot \sqrt{5}\cdot \sqrt{y}}{\sqrt{5}\cdot \sqrt{5}}$
$=\frac{1}{2}\frac{\sqrt{15}\cdot \sqrt{y}}{5}$
$=\frac{\sqrt{15y}}{10}$
Hence, the simplified value of the provided expression is $\frac{\sqrt{15y}}{10}$

Jeffrey Jordon