Solve sqrt{25/frac{3{4}}}59

$$\sqrt{ \frac{ 25 }{ \frac{ 3 }{ 4 } } } 59$$

Evaluate

$$\frac{590\sqrt{3}}{3}\approx 340.636658822$$

Solution Steps

Divide 25 by \frac{3}{4} by multiplying 25 by the reciprocal of \frac{3}{4}.

$$59\sqrt{25\times \frac{4}{3}}$$

Express 25\times \frac{4}{3} as a single fraction.

$$59\sqrt{\frac{25\times 4}{3}}$$

Multiply 25 and 4 to get 100.

$$59\sqrt{\frac{100}{3}}$$

Rewrite the square root of the division \sqrt{\frac{100}{3}} as the division of square roots \frac{\sqrt{100}}{\sqrt{3}}.

$$59\times \frac{\sqrt{100}}{\sqrt{3}}$$

Calculate the square root of 100 and get 10.

$$59\times \frac{10}{\sqrt{3}}$$

Rationalize the denominator of \frac{10}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$59\times \frac{10\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$59\times \frac{10\sqrt{3}}{3}$$

Express 59\times \frac{10\sqrt{3}}{3} as a single fraction.

$$\frac{59\times 10\sqrt{3}}{3}$$

Multiply 59 and 10 to get 590.

$$\frac{590\sqrt{3}}{3}$$