Solve 10sqrt{16/10}

$$10 \sqrt { \frac { 16 } { 10 } }$$

Evaluate

$$4\sqrt{10}\approx 12.649110641$$

Solution Steps

Reduce the fraction \frac{16}{10} to lowest terms by extracting and canceling out 2.

$$10\sqrt{\frac{8}{5}}$$

Rewrite the square root of the division \sqrt{\frac{8}{5}} as the division of square roots \frac{\sqrt{8}}{\sqrt{5}}.

$$10\times \frac{\sqrt{8}}{\sqrt{5}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$10\times \frac{2\sqrt{2}}{\sqrt{5}}$$

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

$$10\times \frac{2\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$10\times \frac{2\sqrt{2}\sqrt{5}}{5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$10\times \frac{2\sqrt{10}}{5}$$

Cancel out 5, the greatest common factor in 10 and 5.

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

Multiply 2 and 2 to get 4.

$$4\sqrt{10}$$