Solve frac{sqrt{6}}{sqrt{5}}*frac{sqrt{10}}{sqrt{3}}

$$\frac{ \sqrt{ 6 } }{ \sqrt{ 5 } } \times \frac{ \sqrt{ 10 } }{ \sqrt{ 3 } }$$

Evaluate

$$2$$

Solution Steps

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

$$\frac{\sqrt{6}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\times \frac{\sqrt{10}}{\sqrt{3}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{6}\sqrt{5}}{5}\times \frac{\sqrt{10}}{\sqrt{3}}$$

To multiply \sqrt{6} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{5}\times \frac{\sqrt{10}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{10}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{30}}{5}\times \frac{\sqrt{10}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{30}}{5}\times \frac{\sqrt{10}\sqrt{3}}{3}$$

To multiply \sqrt{10} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{5}\times \frac{\sqrt{30}}{3}$$

Multiply \frac{\sqrt{30}}{5} times \frac{\sqrt{30}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{30}\sqrt{30}}{5\times 3}$$

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

$$\frac{30}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$\frac{30}{15}$$

Divide 30 by 15 to get 2.

$$2$$

Factor

$$2$$