Solve 2frac{sqrt{6}}{2sqrt{3}}

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

Evaluate

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

Solution Steps

Rationalize the denominator of \frac{\sqrt{6}}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$2\times \frac{\sqrt{6}\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

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

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

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

Multiply 2 and 3 to get 6.

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

Divide 3\sqrt{2} by 6 to get \frac{1}{2}\sqrt{2}.

$$2\times \frac{1}{2}\sqrt{2}$$

Cancel out 2 and 2.

$$\sqrt{2}$$