Solve 2sqrt{7*6/5sqrt{8^2}}

$$2 \sqrt{ 7 \times \frac{ 6 }{ 5 \sqrt{ { 8 }^{ 2 } } } }$$

Evaluate

$$\frac{\sqrt{105}}{5}\approx 2.049390153$$

Solution Steps

Calculate 8 to the power of 2 and get 64.

$$2\sqrt{7\times \frac{6}{5\sqrt{64}}}$$

Calculate the square root of 64 and get 8.

$$2\sqrt{7\times \frac{6}{5\times 8}}$$

Multiply 5 and 8 to get 40.

$$2\sqrt{7\times \frac{6}{40}}$$

Reduce the fraction \frac{6}{40} to lowest terms by extracting and canceling out 2.

$$2\sqrt{7\times \frac{3}{20}}$$

Express 7\times \frac{3}{20} as a single fraction.

$$2\sqrt{\frac{7\times 3}{20}}$$

Multiply 7 and 3 to get 21.

$$2\sqrt{\frac{21}{20}}$$

Rewrite the square root of the division \sqrt{\frac{21}{20}} as the division of square roots \frac{\sqrt{21}}{\sqrt{20}}.

$$2\times \frac{\sqrt{21}}{\sqrt{20}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$2\times \frac{\sqrt{21}}{2\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{21}}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$2\times \frac{\sqrt{21}\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$2\times \frac{\sqrt{21}\sqrt{5}}{2\times 5}$$

To multiply \sqrt{21} and \sqrt{5}, multiply the numbers under the square root.

$$2\times \frac{\sqrt{105}}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$2\times \frac{\sqrt{105}}{10}$$

Cancel out 10, the greatest common factor in 2 and 10.

$$\frac{\sqrt{105}}{5}$$