Solve frac{sqrt{42}}{2sqrt{6}}

$$\frac { \sqrt { 42 } } { 2 \sqrt { 6 } }$$

Evaluate

$$\frac{\sqrt{7}}{2}\approx 1.322875656$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{42}}{2\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{42}\sqrt{6}}{2\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{42}\sqrt{6}}{2\times 6}$$

Factor 42=6\times 7. Rewrite the square root of the product \sqrt{6\times 7} as the product of square roots \sqrt{6}\sqrt{7}.

$$\frac{\sqrt{6}\sqrt{7}\sqrt{6}}{2\times 6}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{6\sqrt{7}}{2\times 6}$$

Multiply 2 and 6 to get 12.

$$\frac{6\sqrt{7}}{12}$$

Divide 6\sqrt{7} by 12 to get \frac{1}{2}\sqrt{7}.

$$\frac{1}{2}\sqrt{7}$$