Solve 14/sqrt{28}

$$\frac { 14 } { \sqrt { 28 } }$$

Evaluate

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

Solution Steps

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

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

Rationalize the denominator of \frac{14}{2\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{14\sqrt{7}}{2\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

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

Cancel out 2\times 7 in both numerator and denominator.

$$\sqrt{7}$$