Question

simplify by rationalizing the denominator.
\\(\frac{5}{3\sqrt{3}}\\)
t symbol (\\(\sqrt{\square}\\)), type
oot\

Explanation:

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

To rationalize the denominator, we multiply the fraction $\frac{5}{3\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ (since $\frac{\sqrt{3}}{\sqrt{3}} = 1$ and multiplying by 1 doesn't change the value of the fraction). So we have:
$\frac{5\times\sqrt{3}}{3\sqrt{3}\times\sqrt{3}}$

Step2: Simplify the denominator

Simplify the denominator $3\sqrt{3}\times\sqrt{3}$. We know that $\sqrt{a}\times\sqrt{a}=a$ (for $a\geq0$), so $\sqrt{3}\times\sqrt{3} = 3$. Then the denominator becomes $3\times3 = 9$. The numerator is $5\sqrt{3}$. So the fraction simplifies to:
$\frac{5\sqrt{3}}{9}$

Answer:

$\frac{5\sqrt{3}}{9}$