Solve 6sqrt{5}-10sqrt{1/5}

$$6 \sqrt{ 5 } -10 \sqrt{ \frac{ 1 }{ 5 } }$$

Evaluate

$$4\sqrt{5}\approx 8.94427191$$

Solution Steps

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

$$6\sqrt{5}-10\times \frac{\sqrt{1}}{\sqrt{5}}$$

Calculate the square root of 1 and get 1.

$$6\sqrt{5}-10\times \frac{1}{\sqrt{5}}$$

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

$$6\sqrt{5}-10\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$6\sqrt{5}-10\times \frac{\sqrt{5}}{5}$$

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

$$6\sqrt{5}-2\sqrt{5}$$

Combine 6\sqrt{5} and -2\sqrt{5} to get 4\sqrt{5}.

$$4\sqrt{5}$$