Question

rationalize the denominator and simplify.
\\(\frac{\sqrt{2}}{\sqrt{3}}\\)

Explanation:

Step1: Multiply numerator and denominator by $\sqrt{3}$

To rationalize the denominator, we multiply the fraction $\frac{\sqrt{2}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ (since multiplying by 1 doesn't change the value). So we get $\frac{\sqrt{2} \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}$.

Step2: Simplify the numerator and denominator

Using the property $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$, the numerator becomes $\sqrt{2 \times 3} = \sqrt{6}$. The denominator becomes $\sqrt{3 \times 3} = \sqrt{9} = 3$. So the simplified fraction is $\frac{\sqrt{6}}{3}$.

Answer:

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