Solve 2sqrt{18}-4sqrt{1/8}+sqrt{32}+0

$$2 \sqrt{ 18 } -4 \sqrt{ \frac{ 1 }{ 8 } } + \sqrt{ 32 } +0$$

Evaluate

$$9\sqrt{2}\approx 12.727922061$$

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}.

$$2\times 3\sqrt{2}-4\sqrt{\frac{1}{8}}+\sqrt{32}+0$$

Multiply 2 and 3 to get 6.

$$6\sqrt{2}-4\sqrt{\frac{1}{8}}+\sqrt{32}+0$$

Rewrite the square root of the division \sqrt{\frac{1}{8}} as the division of square roots \frac{\sqrt{1}}{\sqrt{8}}.

$$6\sqrt{2}-4\times \frac{\sqrt{1}}{\sqrt{8}}+\sqrt{32}+0$$

Calculate the square root of 1 and get 1.

$$6\sqrt{2}-4\times \frac{1}{\sqrt{8}}+\sqrt{32}+0$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$6\sqrt{2}-4\times \frac{1}{2\sqrt{2}}+\sqrt{32}+0$$

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

$$6\sqrt{2}-4\times \frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}+\sqrt{32}+0$$

The square of \sqrt{2} is 2.

$$6\sqrt{2}-4\times \frac{\sqrt{2}}{2\times 2}+\sqrt{32}+0$$

Multiply 2 and 2 to get 4.

$$6\sqrt{2}-4\times \frac{\sqrt{2}}{4}+\sqrt{32}+0$$

Cancel out 4 and 4.

$$6\sqrt{2}-\sqrt{2}+\sqrt{32}+0$$

Combine 6\sqrt{2} and -\sqrt{2} to get 5\sqrt{2}.

$$5\sqrt{2}+\sqrt{32}+0$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$5\sqrt{2}+4\sqrt{2}+0$$

Combine 5\sqrt{2} and 4\sqrt{2} to get 9\sqrt{2}.

$$9\sqrt{2}+0$$

Anything plus zero gives itself.

$$9\sqrt{2}$$