To rationalize the denominator of [tex]\(\frac{1}{\sqrt{7}}\)[/tex], we need to eliminate the square root from the denominator. We do this by multiplying both the numerator and the denominator by [tex]\(\sqrt{7}\)[/tex].
Let's start by writing down the fraction:
[tex]\[
\frac{1}{\sqrt{7}}
\][/tex]
Now, multiply both the numerator and the denominator by [tex]\(\sqrt{7}\)[/tex]:
[tex]\[
\frac{1 \cdot \sqrt{7}}{\sqrt{7} \cdot \sqrt{7}}
\][/tex]
Simplifying the denominator, we know that [tex]\(\sqrt{7} \cdot \sqrt{7} = 7\)[/tex], so we get:
[tex]\[
\frac{\sqrt{7}}{7}
\][/tex]
Thus, the rationalized fraction simplifies to [tex]\(\frac{\sqrt{7}}{7}\)[/tex].
Examining the provided options:
- (A) [tex]\(\frac{\sqrt{7}}{7}\)[/tex]
- (B) [tex]\(\frac{1}{\sqrt{7}}\)[/tex]
- (C) [tex]\(\frac{\sqrt{7}}{49}\)[/tex]
- (D) [tex]\(\frac{1}{7}\)[/tex]
The correct answer is:
[tex]\[
\boxed{\text{A}}
\][/tex]
