Solve (1)(3sqrt{12}-2sqrt{3}+sqrt{48})div2sqrt{3}

$$( 1 ) ( 3 \sqrt { 12 } - 2 \sqrt { 3 } + \sqrt { 48 } ) \div 2 \sqrt { 3 }$$

Evaluate

$$12$$

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}.

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

Multiply 3 and 2 to get 6.

$$\frac{1\left(6\sqrt{3}-2\sqrt{3}+\sqrt{48}\right)}{2}\sqrt{3}$$

Combine 6\sqrt{3} and -2\sqrt{3} to get 4\sqrt{3}.

$$\frac{1\left(4\sqrt{3}+\sqrt{48}\right)}{2}\sqrt{3}$$

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}.

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

Combine 4\sqrt{3} and 4\sqrt{3} to get 8\sqrt{3}.

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

Multiply 1 and 8 to get 8.

$$\frac{8\sqrt{3}}{2}\sqrt{3}$$

Divide 8\sqrt{3} by 2 to get 4\sqrt{3}.

$$4\sqrt{3}\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$4\times 3$$

Multiply 4 and 3 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$