Question

rationalize the denominator and simplify.
\\(\frac{6}{\sqrt{3}}\\)

Explanation:

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

To rationalize the denominator, we multiply the fraction $\frac{6}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$. This gives us $\frac{6\times\sqrt{3}}{\sqrt{3}\times\sqrt{3}}$.

Step2: Simplify the denominator

We know that $\sqrt{a}\times\sqrt{a}=a$ for $a\geq0$. So, $\sqrt{3}\times\sqrt{3} = 3$. The fraction now becomes $\frac{6\sqrt{3}}{3}$.

Step3: Simplify the fraction

Divide 6 by 3. $6\div3 = 2$. So the simplified form is $2\sqrt{3}$.

Answer:

$2\sqrt{3}$