Solve sqrt{39/5*1/27}

$$\sqrt { \frac { 39 } { 5 } \times \frac { 1 } { 27 } }$$

Evaluate

$$\frac{\sqrt{65}}{15}\approx 0.53748385$$

Solution Steps

Multiply \frac{39}{5} times \frac{1}{27} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{39\times 1}{5\times 27}}$$

Do the multiplications in the fraction \frac{39\times 1}{5\times 27}.

$$\sqrt{\frac{39}{135}}$$

Reduce the fraction \frac{39}{135} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{13}{45}}$$

Rewrite the square root of the division \sqrt{\frac{13}{45}} as the division of square roots \frac{\sqrt{13}}{\sqrt{45}}.

$$\frac{\sqrt{13}}{\sqrt{45}}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\frac{\sqrt{13}}{3\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{13}}{3\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{13}\sqrt{5}}{3\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{13}\sqrt{5}}{3\times 5}$$

To multiply \sqrt{13} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{65}}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$\frac{\sqrt{65}}{15}$$