Solve 4sqrt{100/360}

$$4 \sqrt{ \frac{ 100 }{ 360 } }$$

Evaluate

$$\frac{2\sqrt{10}}{3}\approx 2.108185107$$

Solution Steps

Reduce the fraction \frac{100}{360} to lowest terms by extracting and canceling out 20.

$$4\sqrt{\frac{5}{18}}$$

Rewrite the square root of the division \sqrt{\frac{5}{18}} as the division of square roots \frac{\sqrt{5}}{\sqrt{18}}.

$$4\times \frac{\sqrt{5}}{\sqrt{18}}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$4\times \frac{\sqrt{5}}{3\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{5}}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$4\times \frac{\sqrt{5}\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$4\times \frac{\sqrt{5}\sqrt{2}}{3\times 2}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$4\times \frac{\sqrt{10}}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$4\times \frac{\sqrt{10}}{6}$$

Express 4\times \frac{\sqrt{10}}{6} as a single fraction.

$$\frac{4\sqrt{10}}{6}$$

Divide 4\sqrt{10} by 6 to get \frac{2}{3}\sqrt{10}.

$$\frac{2}{3}\sqrt{10}$$