Solve frac{sqrt{12}*sqrt{6}}{sqrt{8}}

$$\frac { \sqrt { 12 } \times \sqrt { 6 } } { \sqrt { 8 } }$$

Evaluate

$$3$$

Solution Steps

Factor 12=6\times 2. Rewrite the square root of the product \sqrt{6\times 2} as the product of square roots \sqrt{6}\sqrt{2}.

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

Multiply \sqrt{6} and \sqrt{6} to get 6.

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

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}.

$$\frac{6\sqrt{2}}{2\sqrt{2}}$$

Cancel out 2\sqrt{2} in both numerator and denominator.

$$3$$

Factor

$$3$$