Solve 164sqrt{5/92}

$$164 \sqrt{ \frac{ 5 }{ 92 } }$$

Evaluate

$$\frac{82\sqrt{115}}{23}\approx 38.232697138$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{92}} as the division of square roots \frac{\sqrt{5}}{\sqrt{92}}.

$$164\times \frac{\sqrt{5}}{\sqrt{92}}$$

Factor 92=2^{2}\times 23. Rewrite the square root of the product \sqrt{2^{2}\times 23} as the product of square roots \sqrt{2^{2}}\sqrt{23}. Take the square root of 2^{2}.

$$164\times \frac{\sqrt{5}}{2\sqrt{23}}$$

Rationalize the denominator of \frac{\sqrt{5}}{2\sqrt{23}} by multiplying numerator and denominator by \sqrt{23}.

$$164\times \frac{\sqrt{5}\sqrt{23}}{2\left(\sqrt{23}\right)^{2}}$$

The square of \sqrt{23} is 23.

$$164\times \frac{\sqrt{5}\sqrt{23}}{2\times 23}$$

To multiply \sqrt{5} and \sqrt{23}, multiply the numbers under the square root.

$$164\times \frac{\sqrt{115}}{2\times 23}$$

Multiply 2 and 23 to get 46.

$$164\times \frac{\sqrt{115}}{46}$$

Express 164\times \frac{\sqrt{115}}{46} as a single fraction.

$$\frac{164\sqrt{115}}{46}$$

Divide 164\sqrt{115} by 46 to get \frac{82}{23}\sqrt{115}.

$$\frac{82}{23}\sqrt{115}$$