Solve sqrt{5/8}divsqrt{11/4}=

$$\sqrt { \frac { 5 } { 8 } } \div \sqrt { 1 \frac { 1 } { 4 } } =$$

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Solution Steps

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

$$\frac{\frac{\sqrt{5}}{\sqrt{8}}}{\sqrt{\frac{1\times 4+1}{4}}}$$

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}.

$$\frac{\frac{\sqrt{5}}{2\sqrt{2}}}{\sqrt{\frac{1\times 4+1}{4}}}$$

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

$$\frac{\frac{\sqrt{5}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}}{\sqrt{\frac{1\times 4+1}{4}}}$$

The square of \sqrt{2} is 2.

$$\frac{\frac{\sqrt{5}\sqrt{2}}{2\times 2}}{\sqrt{\frac{1\times 4+1}{4}}}$$

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

$$\frac{\frac{\sqrt{10}}{2\times 2}}{\sqrt{\frac{1\times 4+1}{4}}}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{\sqrt{10}}{4}}{\sqrt{\frac{1\times 4+1}{4}}}$$

Multiply 1 and 4 to get 4.

$$\frac{\frac{\sqrt{10}}{4}}{\sqrt{\frac{4+1}{4}}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{\sqrt{10}}{4}}{\sqrt{\frac{5}{4}}}$$

Rewrite the square root of the division \sqrt{\frac{5}{4}} as the division of square roots \frac{\sqrt{5}}{\sqrt{4}}.

$$\frac{\frac{\sqrt{10}}{4}}{\frac{\sqrt{5}}{\sqrt{4}}}$$

Calculate the square root of 4 and get 2.

$$\frac{\frac{\sqrt{10}}{4}}{\frac{\sqrt{5}}{2}}$$

Divide \frac{\sqrt{10}}{4} by \frac{\sqrt{5}}{2} by multiplying \frac{\sqrt{10}}{4} by the reciprocal of \frac{\sqrt{5}}{2}.

$$\frac{\sqrt{10}\times 2}{4\sqrt{5}}$$

Cancel out 2 in both numerator and denominator.

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

Rationalize the denominator of \frac{\sqrt{10}}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

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

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

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

Multiply \sqrt{5} and \sqrt{5} to get 5.

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

Multiply 2 and 5 to get 10.

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

Divide 5\sqrt{2} by 10 to get \frac{1}{2}\sqrt{2}.

$$\frac{1}{2}\sqrt{2}$$