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

Formula:
$\sqrt[n]{a}=a^{1/n}$
$(\sqrt[n]{a}{)}^m=\sqrt[n]{a^m}$
${\displaystyle =a^{\frac{m}{n}}}$
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) ${\displaystyle \sqrt{\frac{3y}{20}}=\sqrt{\frac{3y}{5\cdot 4}}}$
${\displaystyle =\sqrt{\frac{3y}{5\cdot 2^2}}}$
${\displaystyle =\frac{1}{2}\sqrt{\frac{3y}{5}}}$
b) ${\displaystyle \sqrt{\frac{3y}{20}}=\frac{1}{2}\sqrt{\frac{3y}{5}}\times \frac{\sqrt{5}}{\sqrt{5}}}$
${\displaystyle =\frac{1}{2}\frac{\sqrt{3}\cdot \sqrt{5}\cdot \sqrt{y}}{\sqrt{5}\cdot \sqrt{5}}}$
${\displaystyle =\frac{1}{2}\frac{\sqrt{15}\cdot \sqrt{y}}{5}}$
${\displaystyle =\frac{\sqrt{15y}}{10}}$
Hence, the simplified value of the provided expression is ${\displaystyle \frac{\sqrt{15y}}{10}}$