Solve sqrt{12}-2(sqrt{27}-1/2sqrt{48})

$$\sqrt { 12 } - 2 ( \sqrt { 27 } - \frac { 1 } { 2 } \sqrt { 48 } )$$

Evaluate

$$0$$

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}.

$$2\sqrt{3}-2\left(\sqrt{27}-\frac{1}{2}\sqrt{48}\right)$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$2\sqrt{3}-2\left(3\sqrt{3}-\frac{1}{2}\sqrt{48}\right)$$

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}.

$$2\sqrt{3}-2\left(3\sqrt{3}-\frac{1}{2}\times 4\sqrt{3}\right)$$

Express -\frac{1}{2}\times 4 as a single fraction.

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

Divide -4 by 2 to get -2.

$$2\sqrt{3}-2\left(3\sqrt{3}-2\sqrt{3}\right)$$

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

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

Combine 2\sqrt{3} and -2\sqrt{3} to get 0.

$$0$$

Factor

$$0$$