Solve frac{2sqrt{6}}{2}+sqrt{75}-3/sqrt{12}

$$\frac { 2 \sqrt { 6 } } { 2 } + \sqrt { 75 } - \frac { 3 } { \sqrt { 12 } }$$

Evaluate

$$\frac{9\sqrt{3}}{2}+\sqrt{6}\approx 10.243718377$$

Solution Steps

Cancel out 2 and 2.

$$\sqrt{6}+\sqrt{75}-\frac{3}{\sqrt{12}}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\sqrt{6}+5\sqrt{3}-\frac{3}{\sqrt{12}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\sqrt{6}+5\sqrt{3}-\frac{3}{2\sqrt{3}}$$

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

$$\sqrt{6}+5\sqrt{3}-\frac{3\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{6}+5\sqrt{3}-\frac{3\sqrt{3}}{2\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\sqrt{6}+5\sqrt{3}-\frac{\sqrt{3}}{2}$$

Combine 5\sqrt{3} and -\frac{\sqrt{3}}{2} to get \frac{9}{2}\sqrt{3}.

$$\sqrt{6}+\frac{9}{2}\sqrt{3}$$