Solve sqrt{14}*sqrt{1/2}=

$$\sqrt{ 14 } \times \sqrt{ \frac{ 1 }{ 2 } } =$$

Evaluate

$$\sqrt{7}\approx 2.645751311$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$\sqrt{14}\times \frac{\sqrt{1}}{\sqrt{2}}$$

Calculate the square root of 1 and get 1.

$$\sqrt{14}\times \frac{1}{\sqrt{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\sqrt{14}\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

Express \sqrt{14}\times \frac{\sqrt{2}}{2} as a single fraction.

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

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}.

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

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

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

Cancel out 2 and 2.

$$\sqrt{7}$$