Solve 2^2sqrt{4/5%6}

$${ 2 }^{ 2 } \sqrt{ \frac{ 4 }{ 5 \% 6 } }$$

Evaluate

$$\frac{8\sqrt{30}}{3}\approx 14.605934867$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$4\sqrt{\frac{4}{\frac{5}{100}\times 6}}$$

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$4\sqrt{\frac{4}{\frac{1}{20}\times 6}}$$

Multiply \frac{1}{20} and 6 to get \frac{6}{20}.

$$4\sqrt{\frac{4}{\frac{6}{20}}}$$

Reduce the fraction \frac{6}{20} to lowest terms by extracting and canceling out 2.

$$4\sqrt{\frac{4}{\frac{3}{10}}}$$

Divide 4 by \frac{3}{10} by multiplying 4 by the reciprocal of \frac{3}{10}.

$$4\sqrt{4\times \frac{10}{3}}$$

Express 4\times \frac{10}{3} as a single fraction.

$$4\sqrt{\frac{4\times 10}{3}}$$

Multiply 4 and 10 to get 40.

$$4\sqrt{\frac{40}{3}}$$

Rewrite the square root of the division \sqrt{\frac{40}{3}} as the division of square roots \frac{\sqrt{40}}{\sqrt{3}}.

$$4\times \frac{\sqrt{40}}{\sqrt{3}}$$

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}.

$$4\times \frac{2\sqrt{10}}{\sqrt{3}}$$

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

$$4\times \frac{2\sqrt{10}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$4\times \frac{2\sqrt{10}\sqrt{3}}{3}$$

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

$$4\times \frac{2\sqrt{30}}{3}$$

Express 4\times \frac{2\sqrt{30}}{3} as a single fraction.

$$\frac{4\times 2\sqrt{30}}{3}$$

Multiply 4 and 2 to get 8.

$$\frac{8\sqrt{30}}{3}$$