Solve 256divsqrt{5/74}

$$256 \div \sqrt{ \frac{ 5 }{ 74 } }$$

Evaluate

$$\frac{256\sqrt{370}}{5}\approx 984.851663958$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{74}} as the division of square roots \frac{\sqrt{5}}{\sqrt{74}}.

$$\frac{256}{\frac{\sqrt{5}}{\sqrt{74}}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{74}} by multiplying numerator and denominator by \sqrt{74}.

$$\frac{256}{\frac{\sqrt{5}\sqrt{74}}{\left(\sqrt{74}\right)^{2}}}$$

The square of \sqrt{74} is 74.

$$\frac{256}{\frac{\sqrt{5}\sqrt{74}}{74}}$$

To multiply \sqrt{5} and \sqrt{74}, multiply the numbers under the square root.

$$\frac{256}{\frac{\sqrt{370}}{74}}$$

Divide 256 by \frac{\sqrt{370}}{74} by multiplying 256 by the reciprocal of \frac{\sqrt{370}}{74}.

$$\frac{256\times 74}{\sqrt{370}}$$

Rationalize the denominator of \frac{256\times 74}{\sqrt{370}} by multiplying numerator and denominator by \sqrt{370}.

$$\frac{256\times 74\sqrt{370}}{\left(\sqrt{370}\right)^{2}}$$

The square of \sqrt{370} is 370.

$$\frac{256\times 74\sqrt{370}}{370}$$

Multiply 256 and 74 to get 18944.

$$\frac{18944\sqrt{370}}{370}$$

Divide 18944\sqrt{370} by 370 to get \frac{256}{5}\sqrt{370}.

$$\frac{256}{5}\sqrt{370}$$