Solve sqrt{21/5}

$$\sqrt { 2 \frac { 1 } { 5 } }$$

Evaluate

$$\frac{\sqrt{55}}{5}\approx 1.483239697$$

Solution Steps

Multiply 2 and 5 to get 10.

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

Add 10 and 1 to get 11.

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

Rewrite the square root of the division \sqrt{\frac{11}{5}} as the division of square roots \frac{\sqrt{11}}{\sqrt{5}}.

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

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

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

The square of \sqrt{5} is 5.

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

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

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