Solve -3sqrt{1/5}

$$-3 \sqrt{ \frac{ 1 }{ 5 } }$$

Evaluate

$$-\frac{3\sqrt{5}}{5}\approx -1.341640786$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

$$-3\times \frac{\sqrt{1}}{\sqrt{5}}$$

Calculate the square root of 1 and get 1.

$$-3\times \frac{1}{\sqrt{5}}$$

Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$-3\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$-3\times \frac{\sqrt{5}}{5}$$

Express -3\times \frac{\sqrt{5}}{5} as a single fraction.

$$\frac{-3\sqrt{5}}{5}$$