Solve frac{85/sqrt{652252}}{}

$$\frac{ \frac{ 85 }{ \sqrt{ 652252 } } }{ }$$

Evaluate

$$\frac{85\sqrt{163063}}{326126}\approx 0.105247361$$

Solution Steps

Factor 652252=2^{2}\times 163063. Rewrite the square root of the product \sqrt{2^{2}\times 163063} as the product of square roots \sqrt{2^{2}}\sqrt{163063}. Take the square root of 2^{2}.

$$\frac{\frac{85}{2\sqrt{163063}}}{1}$$

Rationalize the denominator of \frac{85}{2\sqrt{163063}} by multiplying numerator and denominator by \sqrt{163063}.

$$\frac{\frac{85\sqrt{163063}}{2\left(\sqrt{163063}\right)^{2}}}{1}$$

The square of \sqrt{163063} is 163063.

$$\frac{\frac{85\sqrt{163063}}{2\times 163063}}{1}$$

Multiply 2 and 163063 to get 326126.

$$\frac{\frac{85\sqrt{163063}}{326126}}{1}$$

Anything divided by one gives itself.

$$\frac{85\sqrt{163063}}{326126}$$