Solve =20*sqrt{2/30}

$$= 20 \cdot \sqrt { \frac { 2 } { 30 } }$$

Evaluate

$$\frac{4\sqrt{15}}{3}\approx 5.163977795$$

Solution Steps

Reduce the fraction \frac{2}{30} to lowest terms by extracting and canceling out 2.

$$20\sqrt{\frac{1}{15}}$$

Rewrite the square root of the division \sqrt{\frac{1}{15}} as the division of square roots \frac{\sqrt{1}}{\sqrt{15}}.

$$20\times \frac{\sqrt{1}}{\sqrt{15}}$$

Calculate the square root of 1 and get 1.

$$20\times \frac{1}{\sqrt{15}}$$

Rationalize the denominator of \frac{1}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$20\times \frac{\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$20\times \frac{\sqrt{15}}{15}$$

Express 20\times \frac{\sqrt{15}}{15} as a single fraction.

$$\frac{20\sqrt{15}}{15}$$

Divide 20\sqrt{15} by 15 to get \frac{4}{3}\sqrt{15}.

$$\frac{4}{3}\sqrt{15}$$