Solve sqrt{55*10^3/1.25*10^6}

$$\sqrt { \frac { 55 \times 10 ^ { 3 } } { 1.25 \times 10 ^ { 6 } } }$$

Evaluate

$$\frac{\sqrt{110}}{50}\approx 0.20976177$$

Solution Steps

Cancel out 10^{3} in both numerator and denominator.

$$\sqrt{\frac{55}{1.25\times 10^{3}}}$$

Calculate 10 to the power of 3 and get 1000.

$$\sqrt{\frac{55}{1.25\times 1000}}$$

Multiply 1.25 and 1000 to get 1250.

$$\sqrt{\frac{55}{1250}}$$

Reduce the fraction \frac{55}{1250} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{11}{250}}$$

Rewrite the square root of the division \sqrt{\frac{11}{250}} as the division of square roots \frac{\sqrt{11}}{\sqrt{250}}.

$$\frac{\sqrt{11}}{\sqrt{250}}$$

Factor 250=5^{2}\times 10. Rewrite the square root of the product \sqrt{5^{2}\times 10} as the product of square roots \sqrt{5^{2}}\sqrt{10}. Take the square root of 5^{2}.

$$\frac{\sqrt{11}}{5\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{11}}{5\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{11}\sqrt{10}}{5\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{11}\sqrt{10}}{5\times 10}$$

To multiply \sqrt{11} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{110}}{5\times 10}$$

Multiply 5 and 10 to get 50.

$$\frac{\sqrt{110}}{50}$$