Solve frac{sqrt{96}}{2sqrt{12}}=

$$\frac { \sqrt { 96 } } { 2 \sqrt { 12 } } =$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

$$\frac{4\sqrt{6}}{2\sqrt{12}}$$

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}.

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

Multiply 2 and 2 to get 4.

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

Cancel out 4 in both numerator and denominator.

$$\frac{\sqrt{6}}{\sqrt{3}}$$

Rewrite the division of square roots \frac{\sqrt{6}}{\sqrt{3}} as the square root of the division \sqrt{\frac{6}{3}} and perform the division.

$$\sqrt{2}$$