Solve frac{2sqrt{12}frac{sqrt{3}}{4}}{3}sqrt{2}

$$\frac{ 2 \sqrt{ 12 } \frac{ \sqrt{ 3 } }{ 4 } }{ 3 } \sqrt{ 2 }$$

Evaluate

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

Solution Steps

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}.

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

Multiply 2 and 2 to get 4.

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

Cancel out 4 and 4.

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

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

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

Divide 3 by 3 to get 1.

$$1\sqrt{2}$$

For any term t, t\times 1=t and 1t=t.

$$\sqrt{2}$$