Solve sqrt{5^221/frac{55{}}}

$$\sqrt{ { 5 }^{ 2 } \frac{ 21 }{ \frac{ 55 }{ } } }$$

Evaluate

$$\frac{\sqrt{1155}}{11}\approx 3.089571903$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\sqrt{25\times \frac{21}{\frac{55}{1}}}$$

Divide 21 by \frac{55}{1} by multiplying 21 by the reciprocal of \frac{55}{1}.

$$\sqrt{25\times \frac{21}{55}}$$

Express 25\times \frac{21}{55} as a single fraction.

$$\sqrt{\frac{25\times 21}{55}}$$

Multiply 25 and 21 to get 525.

$$\sqrt{\frac{525}{55}}$$

Reduce the fraction \frac{525}{55} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{105}{11}}$$

Rewrite the square root of the division \sqrt{\frac{105}{11}} as the division of square roots \frac{\sqrt{105}}{\sqrt{11}}.

$$\frac{\sqrt{105}}{\sqrt{11}}$$

Rationalize the denominator of \frac{\sqrt{105}}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$\frac{\sqrt{105}\sqrt{11}}{\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$\frac{\sqrt{105}\sqrt{11}}{11}$$

To multiply \sqrt{105} and \sqrt{11}, multiply the numbers under the square root.

$$\frac{\sqrt{1155}}{11}$$