Solve 5sqrt{7:8}=

$$5 \sqrt { 7 : 8 } =$$

Evaluate

$$\frac{5\sqrt{14}}{4}\approx 4.677071733$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{7}{8}} as the division of square roots \frac{\sqrt{7}}{\sqrt{8}}.

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

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}.

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

Rationalize the denominator of \frac{\sqrt{7}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$5\times \frac{\sqrt{7}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

To multiply \sqrt{7} and \sqrt{2}, multiply the numbers under the square root.

$$5\times \frac{\sqrt{14}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$5\times \frac{\sqrt{14}}{4}$$

Express 5\times \frac{\sqrt{14}}{4} as a single fraction.

$$\frac{5\sqrt{14}}{4}$$