Solve 3sqrt{2}-2sqrt{12}-4sqrt{1/8}

$$3 \sqrt { 2 } - 2 \sqrt { 12 } - 4 \sqrt { \frac { 1 } { 8 } }$$

Evaluate

$$2\sqrt{2}-4\sqrt{3}\approx -4.099776106$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

Multiply -2 and 2 to get -4.

$$3\sqrt{2}-4\sqrt{3}-4\sqrt{\frac{1}{8}}$$

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

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

Calculate the square root of 1 and get 1.

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

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}.

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

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

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

The square of \sqrt{2} is 2.

$$3\sqrt{2}-4\sqrt{3}-4\times \frac{\sqrt{2}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$3\sqrt{2}-4\sqrt{3}-4\times \frac{\sqrt{2}}{4}$$

Cancel out 4 and 4.

$$3\sqrt{2}-4\sqrt{3}-\sqrt{2}$$

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

$$2\sqrt{2}-4\sqrt{3}$$