Solve {left(5sqrt{5/9}right)}^2

$${ \left(5 \sqrt{ \frac{ 5 }{ 9 } } \right) }^{ 2 }$$

Evaluate

$$\frac{125}{9}\approx 13.888888889$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{9}} as the division of square roots \frac{\sqrt{5}}{\sqrt{9}}.

$$\left(5\times \frac{\sqrt{5}}{\sqrt{9}}\right)^{2}$$

Calculate the square root of 9 and get 3.

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

Express 5\times \frac{\sqrt{5}}{3} as a single fraction.

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

To raise \frac{5\sqrt{5}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(5\sqrt{5}\right)^{2}.

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

Calculate 5 to the power of 2 and get 25.

$$\frac{25\left(\sqrt{5}\right)^{2}}{3^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{25\times 5}{3^{2}}$$

Multiply 25 and 5 to get 125.

$$\frac{125}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{125}{9}$$

Factor

$$\frac{5 ^ {3}}{3 ^ {2}} = 13\frac{8}{9} = 13.88888888888889$$