Question

simplify by rationalizing the denominator.
\\(\frac{4}{\sqrt{11}}\\)
bol (\\(\sqrt{\square}\\)), type
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Explanation:

Step1: Multiply numerator and denominator by $\sqrt{11}$

To rationalize the denominator, we multiply the fraction $\frac{4}{\sqrt{11}}$ by $\frac{\sqrt{11}}{\sqrt{11}}$ (since $\frac{\sqrt{11}}{\sqrt{11}} = 1$ and multiplying by 1 doesn't change the value of the fraction). So we get $\frac{4\times\sqrt{11}}{\sqrt{11}\times\sqrt{11}}$.

Step2: Simplify the denominator

We know that $\sqrt{a}\times\sqrt{a}=a$ for $a\geq0$. So $\sqrt{11}\times\sqrt{11} = 11$. Then the fraction becomes $\frac{4\sqrt{11}}{11}$.

Answer:

$\frac{4\sqrt{11}}{11}$