Solve frac{sqrt{8}sqrt{6}}{sqrt{4}}

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

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

Solution Steps

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}.

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

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}.

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

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

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

Calculate the square root of 4 and get 2.

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

Cancel out 2 and 2.

$$2\sqrt{3}$$