Solve sqrt{2(138.072)/3(20)}

$$\sqrt{ \frac{ 2(138.072) }{ 3(20) } }$$

Evaluate

$$\frac{\sqrt{11506}}{50}\approx 2.145320489$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\sqrt{\frac{138.072}{3\times 10}}$$

Multiply 3 and 10 to get 30.

$$\sqrt{\frac{138.072}{30}}$$

Expand \frac{138.072}{30} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{138072}{30000}}$$

Reduce the fraction \frac{138072}{30000} to lowest terms by extracting and canceling out 24.

$$\sqrt{\frac{5753}{1250}}$$

Rewrite the square root of the division \sqrt{\frac{5753}{1250}} as the division of square roots \frac{\sqrt{5753}}{\sqrt{1250}}.

$$\frac{\sqrt{5753}}{\sqrt{1250}}$$

Factor 1250=25^{2}\times 2. Rewrite the square root of the product \sqrt{25^{2}\times 2} as the product of square roots \sqrt{25^{2}}\sqrt{2}. Take the square root of 25^{2}.

$$\frac{\sqrt{5753}}{25\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{5753}}{25\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{5753}\sqrt{2}}{25\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{5753}\sqrt{2}}{25\times 2}$$

To multiply \sqrt{5753} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{11506}}{25\times 2}$$

Multiply 25 and 2 to get 50.

$$\frac{\sqrt{11506}}{50}$$