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

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

Evaluate

$$\frac{2^{\frac{3}{4}}}{2}-\frac{6\sqrt{2}}{2}+2\approx -1.401744272$$

Solution Steps

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}.

$$\sqrt[4]{\frac{1}{2}}-\sqrt{3}\sqrt{2}\sqrt{3}+\frac{\sqrt{12}}{\sqrt{3}}$$

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

$$\sqrt[4]{\frac{1}{2}}-3\sqrt{2}+\frac{\sqrt{12}}{\sqrt{3}}$$

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.

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

Calculate the square root of 4 and get 2.

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