Solve 2sqrt{24}div1/2sqrt{2}div4sqrt{3}

$$2 \sqrt { 24 } \div \frac { 1 } { 2 } \sqrt { 2 } \div 4 \sqrt { 3 }$$

Evaluate

$$12$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{\frac{2\times 2\sqrt{6}}{\frac{1}{2}}\sqrt{2}}{4}\sqrt{3}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{4\sqrt{6}}{\frac{1}{2}}\sqrt{2}}{4}\sqrt{3}$$

Divide 4\sqrt{6} by \frac{1}{2} by multiplying 4\sqrt{6} by the reciprocal of \frac{1}{2}.

$$\frac{4\sqrt{6}\times 2\sqrt{2}}{4}\sqrt{3}$$

Multiply 4 and 2 to get 8.

$$\frac{8\sqrt{6}\sqrt{2}}{4}\sqrt{3}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 8 and 2 to get 16.

$$\frac{16\sqrt{3}}{4}\sqrt{3}$$

Divide 16\sqrt{3} by 4 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

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