Solve -3/sqrt{12}+1/sqrt{4}+sqrt{4}

$$\frac { - 3 } { \sqrt { 12 } } + \frac { 1 } { \sqrt { 4 } } + \sqrt { 4 }$$

Evaluate

$$\frac{5-\sqrt{3}}{2}\approx 1.633974596$$

Short Solution Steps

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}.

$$\frac{-3}{2\sqrt{3}}+\frac{1}{\sqrt{4}}+\sqrt{4}$$

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

$$\frac{-3\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}+\frac{1}{\sqrt{4}}+\sqrt{4}$$

The square of \sqrt{3} is 3.

$$\frac{-3\sqrt{3}}{2\times 3}+\frac{1}{\sqrt{4}}+\sqrt{4}$$

Cancel out 3 in both numerator and denominator.

$$\frac{-\sqrt{3}}{2}+\frac{1}{\sqrt{4}}+\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$\frac{-\sqrt{3}}{2}+\frac{1}{2}+\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$\frac{-\sqrt{3}}{2}+\frac{1}{2}+2$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{-\sqrt{3}}{2}+\frac{1}{2}+\frac{4}{2}$$

Since \frac{1}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

$$\frac{-\sqrt{3}}{2}+\frac{1+4}{2}$$

Add 1 and 4 to get 5.

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

Since \frac{-\sqrt{3}}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

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