Solve 4720sqrt{frac{222/5555}}{}

$$\frac{ 4720 \sqrt{ \frac{ 222 }{ 5555 } } }{ }$$

Evaluate

$$\frac{944\sqrt{1233210}}{1111}\approx 943.575061874$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{222}{5555}} as the division of square roots \frac{\sqrt{222}}{\sqrt{5555}}.

$$\frac{4720\times \frac{\sqrt{222}}{\sqrt{5555}}}{1}$$

Rationalize the denominator of \frac{\sqrt{222}}{\sqrt{5555}} by multiplying numerator and denominator by \sqrt{5555}.

$$\frac{4720\times \frac{\sqrt{222}\sqrt{5555}}{\left(\sqrt{5555}\right)^{2}}}{1}$$

The square of \sqrt{5555} is 5555.

$$\frac{4720\times \frac{\sqrt{222}\sqrt{5555}}{5555}}{1}$$

To multiply \sqrt{222} and \sqrt{5555}, multiply the numbers under the square root.

$$\frac{4720\times \frac{\sqrt{1233210}}{5555}}{1}$$

Express 4720\times \frac{\sqrt{1233210}}{5555} as a single fraction.

$$\frac{\frac{4720\sqrt{1233210}}{5555}}{1}$$

Anything divided by one gives itself.

$$\frac{4720\sqrt{1233210}}{5555}$$

Divide 4720\sqrt{1233210} by 5555 to get \frac{944}{1111}\sqrt{1233210}.

$$\frac{944}{1111}\sqrt{1233210}$$