Solve frac{sqrt{20*6}}{sqrt{2*15}}

$$\frac{ \sqrt{ 20 \cdot 6 } }{ \sqrt{ 2 \times 15 } }$$

Evaluate

$$2$$

Solution Steps

Multiply 20 and 6 to get 120.

$$\frac{\sqrt{120}}{\sqrt{2\times 15}}$$

Factor 120=2^{2}\times 30. Rewrite the square root of the product \sqrt{2^{2}\times 30} as the product of square roots \sqrt{2^{2}}\sqrt{30}. Take the square root of 2^{2}.

$$\frac{2\sqrt{30}}{\sqrt{2\times 15}}$$

Multiply 2 and 15 to get 30.

$$\frac{2\sqrt{30}}{\sqrt{30}}$$

Rationalize the denominator of \frac{2\sqrt{30}}{\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$\frac{2\sqrt{30}\sqrt{30}}{\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$\frac{2\sqrt{30}\sqrt{30}}{30}$$

Multiply \sqrt{30} and \sqrt{30} to get 30.

$$\frac{2\times 30}{30}$$

Multiply 2 and 30 to get 60.

$$\frac{60}{30}$$

Divide 60 by 30 to get 2.

$$2$$

Factor

$$2$$