Solve 4sqrt{9div6}

$$4 \sqrt{ 9 \div 6 }$$

Evaluate

$$2\sqrt{6}\approx 4.898979486$$

Solution Steps

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$4\sqrt{\frac{3}{2}}$$

Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.

$$4\times \frac{\sqrt{3}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$4\times \frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$4\times \frac{\sqrt{3}\sqrt{2}}{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$4\times \frac{\sqrt{6}}{2}$$

Cancel out 2, the greatest common factor in 4 and 2.

$$2\sqrt{6}$$