Solve sqrt{3-6/5}=

$$\sqrt{ 3- \frac{ 6 }{ 5 } } =$$

Evaluate

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

Solution Steps

Convert 3 to fraction \frac{15}{5}.

$$\sqrt{\frac{15}{5}-\frac{6}{5}}$$

Since \frac{15}{5} and \frac{6}{5} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{15-6}{5}}$$

Subtract 6 from 15 to get 9.

$$\sqrt{\frac{9}{5}}$$

Rewrite the square root of the division \sqrt{\frac{9}{5}} as the division of square roots \frac{\sqrt{9}}{\sqrt{5}}.

$$\frac{\sqrt{9}}{\sqrt{5}}$$

Calculate the square root of 9 and get 3.

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

Rationalize the denominator of \frac{3}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

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