Solve 12sqrt{5*9/5^2}

$$12 \sqrt{ 5 \times \frac{ 9 }{ { 5 }^{ 2 } } }$$

Evaluate

$$\frac{36\sqrt{5}}{5}\approx 16.099689438$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$12\sqrt{5\times \frac{9}{25}}$$

Express 5\times \frac{9}{25} as a single fraction.

$$12\sqrt{\frac{5\times 9}{25}}$$

Multiply 5 and 9 to get 45.

$$12\sqrt{\frac{45}{25}}$$

Reduce the fraction \frac{45}{25} to lowest terms by extracting and canceling out 5.

$$12\sqrt{\frac{9}{5}}$$

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

$$12\times \frac{\sqrt{9}}{\sqrt{5}}$$

Calculate the square root of 9 and get 3.

$$12\times \frac{3}{\sqrt{5}}$$

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

$$12\times \frac{3\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$12\times \frac{3\sqrt{5}}{5}$$

Express 12\times \frac{3\sqrt{5}}{5} as a single fraction.

$$\frac{12\times 3\sqrt{5}}{5}$$

Multiply 12 and 3 to get 36.

$$\frac{36\sqrt{5}}{5}$$