Solve sqrt{12+3/4+6}

$$\sqrt{ \frac{ 12+3 }{ 4+6 } }$$

Evaluate

$$\frac{\sqrt{6}}{2}\approx 1.224744871$$

Solution Steps

Add 12 and 3 to get 15.

$$\sqrt{\frac{15}{4+6}}$$

Add 4 and 6 to get 10.

$$\sqrt{\frac{15}{10}}$$

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

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

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

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

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

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

The square of \sqrt{2} is 2.

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

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

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