Rationalize the denominator of [tex]\frac{1}{\sqrt{7}}[/tex].

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]



Answer :

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]