Solve frac{8sqrt{12}}{2sqrt{3}}

$$\frac{ 8 \sqrt{ 12 } }{ 2 \sqrt{ 3 } }$$

Evaluate

$$8$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{4\sqrt{12}}{\sqrt{3}}$$

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}.

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

Multiply 4 and 2 to get 8.

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

Rationalize the denominator of \frac{8\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{8\sqrt{3}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

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

$$\frac{8\times 3}{3}$$

Multiply 8 and 3 to get 24.

$$\frac{24}{3}$$

Divide 24 by 3 to get 8.

$$8$$

Factor

$$2^{3}$$