Solve frac{12sqrt{45}}{sqrt{5}}=

$$\frac { 12 \sqrt { 45 } } { \sqrt { 5 } } =$$

Evaluate

$$36$$

Solution Steps

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

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

Multiply 12 and 3 to get 36.

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

Rationalize the denominator of \frac{36\sqrt{5}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{36\sqrt{5}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

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

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

$$\frac{36\times 5}{5}$$

Multiply 36 and 5 to get 180.

$$\frac{180}{5}$$

Divide 180 by 5 to get 36.

$$36$$

Factor

$$2^{2}\times 3^{2}$$