Solve 2sqrt{12}-4sqrt{1/8}+3sqrt{48}

$$2 \sqrt { 12 } - 4 \sqrt { \frac { 1 } { 8 } } + 3 \sqrt { 48 }$$

Evaluate

$$16\sqrt{3}-\sqrt{2}\approx 26.298599359$$

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}.

$$2\times 2\sqrt{3}-4\sqrt{\frac{1}{8}}+3\sqrt{48}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{3}-4\sqrt{\frac{1}{8}}+3\sqrt{48}$$

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

$$4\sqrt{3}-4\times \frac{\sqrt{1}}{\sqrt{8}}+3\sqrt{48}$$

Calculate the square root of 1 and get 1.

$$4\sqrt{3}-4\times \frac{1}{\sqrt{8}}+3\sqrt{48}$$

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}.

$$4\sqrt{3}-4\times \frac{1}{2\sqrt{2}}+3\sqrt{48}$$

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

$$4\sqrt{3}-4\times \frac{\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}+3\sqrt{48}$$

The square of \sqrt{2} is 2.

$$4\sqrt{3}-4\times \frac{\sqrt{2}}{2\times 2}+3\sqrt{48}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{3}-4\times \frac{\sqrt{2}}{4}+3\sqrt{48}$$

Cancel out 4 and 4.

$$4\sqrt{3}-\sqrt{2}+3\sqrt{48}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

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

Multiply 3 and 4 to get 12.

$$4\sqrt{3}-\sqrt{2}+12\sqrt{3}$$

Combine 4\sqrt{3} and 12\sqrt{3} to get 16\sqrt{3}.

$$16\sqrt{3}-\sqrt{2}$$