Questions: Rationalize sqrt(3)/sqrt(2) (or sqrt(3)/sqrt(2)) Choose one · 3 points sqrt(3) sqrt(2) sqrt(6)/2 sqrt(2)/6 sqrt(6)/3 sqrt(3)/6 2/3 3/2 6

Transcript text: Rationalize $\frac{\sqrt{3}}{\sqrt{2}}$ (or sqrt(3)/sqrt(2)) Choose one $\cdot 3$ points $\sqrt{3}$ $\sqrt{2}$ $\frac{\sqrt{6}}{2}$ $\frac{\sqrt{2}}{6}$ $\frac{\sqrt{6}}{3}$ $\frac{\sqrt{3}}{6}$ $\frac{2}{3}$ $\frac{3}{2}$ 6

Solution

Solution Steps

To rationalize the expression $\frac{\sqrt{3}}{\sqrt{2}}$, we need to eliminate the square root in the denominator. This can be done by multiplying both the numerator and the denominator by $\sqrt{2}$.

Step 1: Rationalizing the Expression

To rationalize the expression $\frac{\sqrt{3}}{\sqrt{2}}$, we multiply both the numerator and the denominator by $\sqrt{2}$:

\[ \frac{\sqrt{3}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{3} \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{\sqrt{6}}{2} \]

Step 2: Simplifying the Expression

The expression $\frac{\sqrt{6}}{2}$ is already in its simplest form, as the numerator and denominator have no common factors.