Solve 3sqrt{27/13}

$$3 \sqrt { \frac { 27 } { 13 } }$$

Evaluate

$$\frac{9\sqrt{39}}{13}\approx 4.323460153$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{27}{13}} as the division of square roots \frac{\sqrt{27}}{\sqrt{13}}.

$$3\times \frac{\sqrt{27}}{\sqrt{13}}$$

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}.

$$3\times \frac{3\sqrt{3}}{\sqrt{13}}$$

Rationalize the denominator of \frac{3\sqrt{3}}{\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$3\times \frac{3\sqrt{3}\sqrt{13}}{\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$3\times \frac{3\sqrt{3}\sqrt{13}}{13}$$

To multiply \sqrt{3} and \sqrt{13}, multiply the numbers under the square root.

$$3\times \frac{3\sqrt{39}}{13}$$

Express 3\times \frac{3\sqrt{39}}{13} as a single fraction.

$$\frac{3\times 3\sqrt{39}}{13}$$

Multiply 3 and 3 to get 9.

$$\frac{9\sqrt{39}}{13}$$