Solve 10sqrt{1/5}

$$10 \sqrt { \frac { 1 } { 5 } }$$

Evaluate

$$2\sqrt{5}\approx 4.472135955$$

Solution Steps

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

$$10\times \frac{\sqrt{1}}{\sqrt{5}}$$

Calculate the square root of 1 and get 1.

$$10\times \frac{1}{\sqrt{5}}$$

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

$$10\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$10\times \frac{\sqrt{5}}{5}$$

Cancel out 5, the greatest common factor in 10 and 5.

$$2\sqrt{5}$$