Solve frac{sqrt{2}sqrt{14}}{sqrt{7}}

$$\frac{ \sqrt{ 2 } \sqrt{ 14 } }{ \sqrt{ 7 } }$$

Evaluate

$$2$$

Solution Steps

Factor 14=2\times 7. Rewrite the square root of the product \sqrt{2\times 7} as the product of square roots \sqrt{2}\sqrt{7}.

$$\frac{\sqrt{2}\sqrt{2}\sqrt{7}}{\sqrt{7}}$$

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

$$\frac{2\sqrt{7}}{\sqrt{7}}$$

Rationalize the denominator of \frac{2\sqrt{7}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{2\sqrt{7}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{2\sqrt{7}\sqrt{7}}{7}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$\frac{2\times 7}{7}$$

Multiply 2 and 7 to get 14.

$$\frac{14}{7}$$

Divide 14 by 7 to get 2.

$$2$$

Factor

$$2$$