Solve sqrt{27/11}

$$\sqrt { \frac { 27 } { 11 } }$$

Evaluate

$$\frac{3\sqrt{33}}{11}\approx 1.566698904$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{27}{11}} as the division of square roots \frac{\sqrt{27}}{\sqrt{11}}.

$$\frac{\sqrt{27}}{\sqrt{11}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{3\sqrt{3}}{\sqrt{11}}$$

Rationalize the denominator of \frac{3\sqrt{3}}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$\frac{3\sqrt{3}\sqrt{11}}{\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$\frac{3\sqrt{3}\sqrt{11}}{11}$$

To multiply \sqrt{3} and \sqrt{11}, multiply the numbers under the square root.

$$\frac{3\sqrt{33}}{11}$$