Question

1. simplify the fraction by rationalizing the denominator:

\\(\frac{1}{\sqrt{7}}\\)
\\(\bigcirc\\) a \\(\sqrt{7}\\)
\\(\bigcirc\\) b \\(\frac{\sqrt{7}}{7}\\)
\\(\bigcirc\\) c 7
\\(\bigcirc\\) d \\(\frac{7}{\sqrt{7}}\\)

Explanation:

Step1: Multiply numerator and denominator by $\sqrt{7}$

To rationalize the denominator of $\frac{1}{\sqrt{7}}$, we multiply both the numerator and the denominator by $\sqrt{7}$ (since $\sqrt{a}\times\sqrt{a}=a$ for $a\geq0$). So we have $\frac{1\times\sqrt{7}}{\sqrt{7}\times\sqrt{7}}$.

Step2: Simplify the denominator

Simplify the denominator: $\sqrt{7}\times\sqrt{7} = 7$. The numerator is $1\times\sqrt{7}=\sqrt{7}$. So the fraction becomes $\frac{\sqrt{7}}{7}$.

Answer:

B. $\frac{\sqrt{7}}{7}$