Solve 7sqrt{1/7}

$$7 \sqrt{ \frac{ 1 }{ 7 } }$$

Evaluate

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

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{7}} as the division of square roots \frac{\sqrt{1}}{\sqrt{7}}.

$$7\times \frac{\sqrt{1}}{\sqrt{7}}$$

Calculate the square root of 1 and get 1.

$$7\times \frac{1}{\sqrt{7}}$$

Rationalize the denominator of \frac{1}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

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

The square of \sqrt{7} is 7.

$$7\times \frac{\sqrt{7}}{7}$$

Cancel out 7 and 7.

$$\sqrt{7}$$