Solve sqrt{1220/480*852/340}*100

$$\sqrt { \frac { 1220 } { 480 } \times \frac { 852 } { 340 } } \times 100$$

Evaluate

$$\frac{5\sqrt{736270}}{17}\approx 252.371108629$$

Solution Steps

Reduce the fraction \frac{1220}{480} to lowest terms by extracting and canceling out 20.

$$100\sqrt{\frac{61}{24}\times \frac{852}{340}}$$

Reduce the fraction \frac{852}{340} to lowest terms by extracting and canceling out 4.

$$100\sqrt{\frac{61}{24}\times \frac{213}{85}}$$

Multiply \frac{61}{24} times \frac{213}{85} by multiplying numerator times numerator and denominator times denominator.

$$100\sqrt{\frac{61\times 213}{24\times 85}}$$

Do the multiplications in the fraction \frac{61\times 213}{24\times 85}.

$$100\sqrt{\frac{12993}{2040}}$$

Reduce the fraction \frac{12993}{2040} to lowest terms by extracting and canceling out 3.

$$100\sqrt{\frac{4331}{680}}$$

Rewrite the square root of the division \sqrt{\frac{4331}{680}} as the division of square roots \frac{\sqrt{4331}}{\sqrt{680}}.

$$100\times \frac{\sqrt{4331}}{\sqrt{680}}$$

Factor 680=2^{2}\times 170. Rewrite the square root of the product \sqrt{2^{2}\times 170} as the product of square roots \sqrt{2^{2}}\sqrt{170}. Take the square root of 2^{2}.

$$100\times \frac{\sqrt{4331}}{2\sqrt{170}}$$

Rationalize the denominator of \frac{\sqrt{4331}}{2\sqrt{170}} by multiplying numerator and denominator by \sqrt{170}.

$$100\times \frac{\sqrt{4331}\sqrt{170}}{2\left(\sqrt{170}\right)^{2}}$$

The square of \sqrt{170} is 170.

$$100\times \frac{\sqrt{4331}\sqrt{170}}{2\times 170}$$

To multiply \sqrt{4331} and \sqrt{170}, multiply the numbers under the square root.

$$100\times \frac{\sqrt{736270}}{2\times 170}$$

Multiply 2 and 170 to get 340.

$$100\times \frac{\sqrt{736270}}{340}$$

Express 100\times \frac{\sqrt{736270}}{340} as a single fraction.

$$\frac{100\sqrt{736270}}{340}$$

Divide 100\sqrt{736270} by 340 to get \frac{5}{17}\sqrt{736270}.

$$\frac{5}{17}\sqrt{736270}$$