Solve sqrt{27/40}

$$\sqrt{ \frac{ 27 }{ 40 } }$$

Evaluate

$$\frac{3\sqrt{30}}{20}\approx 0.821583836$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{27}{40}} as the division of square roots \frac{\sqrt{27}}{\sqrt{40}}.

$$\frac{\sqrt{27}}{\sqrt{40}}$$

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}.

$$\frac{3\sqrt{3}}{\sqrt{40}}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\frac{3\sqrt{3}}{2\sqrt{10}}$$

Rationalize the denominator of \frac{3\sqrt{3}}{2\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{3\sqrt{3}\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{3\sqrt{3}\sqrt{10}}{2\times 10}$$

To multiply \sqrt{3} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{3\sqrt{30}}{2\times 10}$$

Multiply 2 and 10 to get 20.

$$\frac{3\sqrt{30}}{20}$$