Solve 4sqrt{1/2}-sqrt{6}*sqrt{3}+sqrt{12}divsqrt{3}

$$4 \sqrt { \frac { 1 } { 2 } } - \sqrt { 6 } \times \sqrt { 3 } + \sqrt { 12 } \div \sqrt { 3 }$$

Evaluate

$$2-\sqrt{2}\approx 0.585786438$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$4\times \frac{\sqrt{1}}{\sqrt{2}}-\sqrt{6}\sqrt{3}+\frac{\sqrt{12}}{\sqrt{3}}$$

Calculate the square root of 1 and get 1.

$$4\times \frac{1}{\sqrt{2}}-\sqrt{6}\sqrt{3}+\frac{\sqrt{12}}{\sqrt{3}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$4\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\sqrt{6}\sqrt{3}+\frac{\sqrt{12}}{\sqrt{3}}$$

The square of \sqrt{2} is 2.

$$4\times \frac{\sqrt{2}}{2}-\sqrt{6}\sqrt{3}+\frac{\sqrt{12}}{\sqrt{3}}$$

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

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

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

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

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

Rewrite the division of square roots \frac{\sqrt{12}}{\sqrt{3}} as the square root of the division \sqrt{\frac{12}{3}} and perform the division.

$$-\sqrt{2}+\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$-\sqrt{2}+2$$