Solve 2sqrt{18}-6*sqrt{1/2}+sqrt[3]{27}

$$2 \sqrt { 18 } - 6 \times \sqrt { \frac { 1 } { 2 } } + \sqrt[ 3 ] { 27 }$$

Evaluate

$$3\left(\sqrt{2}+1\right)\approx 7.242640687$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$2\times 3\sqrt{2}-6\sqrt{\frac{1}{2}}+\sqrt[3]{27}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{2}-6\sqrt{\frac{1}{2}}+\sqrt[3]{27}$$

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

$$6\sqrt{2}-6\times \frac{\sqrt{1}}{\sqrt{2}}+\sqrt[3]{27}$$

Calculate the square root of 1 and get 1.

$$6\sqrt{2}-6\times \frac{1}{\sqrt{2}}+\sqrt[3]{27}$$

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

$$6\sqrt{2}-6\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\sqrt[3]{27}$$

The square of \sqrt{2} is 2.

$$6\sqrt{2}-6\times \frac{\sqrt{2}}{2}+\sqrt[3]{27}$$

Cancel out 2, the greatest common factor in 6 and 2.

$$6\sqrt{2}-3\sqrt{2}+\sqrt[3]{27}$$

Combine 6\sqrt{2} and -3\sqrt{2} to get 3\sqrt{2}.

$$3\sqrt{2}+\sqrt[3]{27}$$

Calculate \sqrt[3]{27} and get 3.

$$3\sqrt{2}+3$$