Solve 2sqrt{2(32)/2.8}

$$2 \sqrt{ \frac{ 2(32) }{ 2.8 } }$$

Evaluate

$$\frac{8\sqrt{70}}{7}\approx 9.561828875$$

Solution Steps

Multiply 2 and 32 to get 64.

$$2\sqrt{\frac{64}{2.8}}$$

Expand \frac{64}{2.8} by multiplying both numerator and the denominator by 10.

$$2\sqrt{\frac{640}{28}}$$

Reduce the fraction \frac{640}{28} to lowest terms by extracting and canceling out 4.

$$2\sqrt{\frac{160}{7}}$$

Rewrite the square root of the division \sqrt{\frac{160}{7}} as the division of square roots \frac{\sqrt{160}}{\sqrt{7}}.

$$2\times \frac{\sqrt{160}}{\sqrt{7}}$$

Factor 160=4^{2}\times 10. Rewrite the square root of the product \sqrt{4^{2}\times 10} as the product of square roots \sqrt{4^{2}}\sqrt{10}. Take the square root of 4^{2}.

$$2\times \frac{4\sqrt{10}}{\sqrt{7}}$$

Rationalize the denominator of \frac{4\sqrt{10}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$2\times \frac{4\sqrt{10}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$2\times \frac{4\sqrt{10}\sqrt{7}}{7}$$

To multiply \sqrt{10} and \sqrt{7}, multiply the numbers under the square root.

$$2\times \frac{4\sqrt{70}}{7}$$

Express 2\times \frac{4\sqrt{70}}{7} as a single fraction.

$$\frac{2\times 4\sqrt{70}}{7}$$

Multiply 2 and 4 to get 8.

$$\frac{8\sqrt{70}}{7}$$