Solve sqrt{125/27}

$$\sqrt { \frac { 125 } { 27 } }$$

Evaluate

$$\frac{5\sqrt{15}}{9}\approx 2.151657415$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{125}{27}} as the division of square roots \frac{\sqrt{125}}{\sqrt{27}}.

$$\frac{\sqrt{125}}{\sqrt{27}}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$\frac{5\sqrt{5}}{\sqrt{27}}$$

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}.

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

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

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

The square of \sqrt{3} is 3.

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

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{5\sqrt{15}}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$\frac{5\sqrt{15}}{9}$$