Solve sqrt{22div7}

$$\sqrt{ 22 \div 7 }$$

Evaluate

$$\frac{\sqrt{154}}{7}\approx 1.772810521$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{22}{7}} as the division of square roots \frac{\sqrt{22}}{\sqrt{7}}.

$$\frac{\sqrt{22}}{\sqrt{7}}$$

Rationalize the denominator of \frac{\sqrt{22}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\sqrt{22}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{\sqrt{22}\sqrt{7}}{7}$$

To multiply \sqrt{22} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{\sqrt{154}}{7}$$