Solve 5sqrt{2*8/5}

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

Evaluate

$$4\sqrt{5}\approx 8.94427191$$

Solution Steps

Express 2\times \frac{8}{5} as a single fraction.

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

Multiply 2 and 8 to get 16.

$$5\sqrt{\frac{16}{5}}$$

Rewrite the square root of the division \sqrt{\frac{16}{5}} as the division of square roots \frac{\sqrt{16}}{\sqrt{5}}.

$$5\times \frac{\sqrt{16}}{\sqrt{5}}$$

Calculate the square root of 16 and get 4.

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

Rationalize the denominator of \frac{4}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$5\times \frac{4\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

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

Cancel out 5 and 5.

$$4\sqrt{5}$$