Solve frac{sqrt{2}sqrt{10}}{sqrt{5}}

$$\frac { \sqrt { 2 } \sqrt { 10 } } { \sqrt { 5 } }$$

Evaluate

$$2$$

Solution Steps

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Rationalize the denominator of \frac{2\sqrt{5}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

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

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

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

Multiply 2 and 5 to get 10.

$$\frac{10}{5}$$

Divide 10 by 5 to get 2.

$$2$$

Factor

$$2$$