Question

simplify by rationalizing the denominator.
\\(\frac{7}{\sqrt{396}}\\)

Explanation:

Step1: Simplify the square root in the denominator

First, factorize \( 396 \) to simplify \( \sqrt{396} \). We know that \( 396 = 4\times9\times11 \), so \( \sqrt{396}=\sqrt{4\times9\times11}=\sqrt{4}\times\sqrt{9}\times\sqrt{11}=2\times3\times\sqrt{11} = 6\sqrt{11} \). So the original fraction becomes \( \frac{7}{6\sqrt{11}} \).

Step2: Rationalize the denominator

To rationalize the denominator, we multiply the numerator and the denominator by \( \sqrt{11} \). So we have \( \frac{7\times\sqrt{11}}{6\sqrt{11}\times\sqrt{11}} \).

Step3: Simplify the denominator

Since \( \sqrt{11}\times\sqrt{11}=11 \), the denominator becomes \( 6\times11 = 66 \), and the numerator is \( 7\sqrt{11} \). So the simplified form is \( \frac{7\sqrt{11}}{66} \).

Answer:

\( \frac{7\sqrt{11}}{66} \)