Solve sqrt{9-1/5}

$$\sqrt { 9 - \frac { 1 } { 5 } }$$

Evaluate

$$\frac{2\sqrt{55}}{5}\approx 2.966479395$$

Solution Steps

Convert 9 to fraction \frac{45}{5}.

$$\sqrt{\frac{45}{5}-\frac{1}{5}}$$

Since \frac{45}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{45-1}{5}}$$

Subtract 1 from 45 to get 44.

$$\sqrt{\frac{44}{5}}$$

Rewrite the square root of the division \sqrt{\frac{44}{5}} as the division of square roots \frac{\sqrt{44}}{\sqrt{5}}.

$$\frac{\sqrt{44}}{\sqrt{5}}$$

Factor 44=2^{2}\times 11. Rewrite the square root of the product \sqrt{2^{2}\times 11} as the product of square roots \sqrt{2^{2}}\sqrt{11}. Take the square root of 2^{2}.

$$\frac{2\sqrt{11}}{\sqrt{5}}$$

Rationalize the denominator of \frac{2\sqrt{11}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{2\sqrt{11}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{2\sqrt{11}\sqrt{5}}{5}$$

To multiply \sqrt{11} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{2\sqrt{55}}{5}$$