Solve frac{9sqrt{20}}{3sqrt{5}}

$$\frac { 9 \sqrt { 20 } } { 3 \sqrt { 5 } }$$

Evaluate

$$6$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{3\sqrt{20}}{\sqrt{5}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

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

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{5}}{\sqrt{5}}$$

Rationalize the denominator of \frac{6\sqrt{5}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{6\sqrt{5}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{6\sqrt{5}\sqrt{5}}{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{6\times 5}{5}$$

Multiply 6 and 5 to get 30.

$$\frac{30}{5}$$

Divide 30 by 5 to get 6.

$$6$$

Factor

$$2\times 3$$