Solve 1/2(sqrt[6]{2})-3sqrt{98}+sqrt{6}*sqrt{12}

$$\frac { 1 } { 2 } ( \sqrt[ 6 ] { 2 } ) - 3 \sqrt { 98 } + \sqrt { 6 } \times \sqrt { 12 }$$

Evaluate

$$\frac{\sqrt[6]{2}}{2}-15\sqrt{2}\approx -20.651972411$$

Solution Steps

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$\frac{1}{2}\sqrt[6]{2}-3\times 7\sqrt{2}+\sqrt{6}\sqrt{12}$$

Multiply -3 and 7 to get -21.

$$\frac{1}{2}\sqrt[6]{2}-21\sqrt{2}+\sqrt{6}\sqrt{12}$$

Factor 12=6\times 2. Rewrite the square root of the product \sqrt{6\times 2} as the product of square roots \sqrt{6}\sqrt{2}.

$$\frac{1}{2}\sqrt[6]{2}-21\sqrt{2}+\sqrt{6}\sqrt{6}\sqrt{2}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{1}{2}\sqrt[6]{2}-21\sqrt{2}+6\sqrt{2}$$

Combine -21\sqrt{2} and 6\sqrt{2} to get -15\sqrt{2}.

$$\frac{1}{2}\sqrt[6]{2}-15\sqrt{2}$$

Factor

$$\frac{1 - 15 \cdot 2 ^ {\frac{4}{3}}}{2 ^ {\frac{5}{6}}} = -20.65197241144174$$