Solve sqrt{frac{275/27}}{5}

$$\frac{ \sqrt{ \frac{ 275 }{ 27 } } }{ 5 }$$

Evaluate

$$\frac{\sqrt{33}}{9}\approx 0.638284739$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{275}{27}} as the division of square roots \frac{\sqrt{275}}{\sqrt{27}}.

$$\frac{\frac{\sqrt{275}}{\sqrt{27}}}{5}$$

Factor 275=5^{2}\times 11. Rewrite the square root of the product \sqrt{5^{2}\times 11} as the product of square roots \sqrt{5^{2}}\sqrt{11}. Take the square root of 5^{2}.

$$\frac{\frac{5\sqrt{11}}{\sqrt{27}}}{5}$$

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}.

$$\frac{\frac{5\sqrt{11}}{3\sqrt{3}}}{5}$$

Rationalize the denominator of \frac{5\sqrt{11}}{3\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\frac{5\sqrt{11}\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}}{5}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{5\sqrt{11}\sqrt{3}}{3\times 3}}{5}$$

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

$$\frac{\frac{5\sqrt{33}}{3\times 3}}{5}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{5\sqrt{33}}{9}}{5}$$

Express \frac{\frac{5\sqrt{33}}{9}}{5} as a single fraction.

$$\frac{5\sqrt{33}}{9\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\sqrt{33}}{9}$$