Solve sqrt{10.000:16}=

$$\sqrt { 10.000 : 16 } =$$

Evaluate

$$\frac{\sqrt{10}}{4}\approx 0.790569415$$

Solution Steps

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

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

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

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

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}.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Multiply 2 and 2 to get 4.

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