Solve 12sqrt{21/2}

$$12 \sqrt{ \frac{ 21 }{ 2 } }$$

Evaluate

$$6\sqrt{42}\approx 38.88444419$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{21}{2}} as the division of square roots \frac{\sqrt{21}}{\sqrt{2}}.

$$12\times \frac{\sqrt{21}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{21}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$12\times \frac{\sqrt{21}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$12\times \frac{\sqrt{21}\sqrt{2}}{2}$$

To multiply \sqrt{21} and \sqrt{2}, multiply the numbers under the square root.

$$12\times \frac{\sqrt{42}}{2}$$

Cancel out 2, the greatest common factor in 12 and 2.

$$6\sqrt{42}$$