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The given expression is:

\[
\frac{1}{\sqrt{7}}
\]

We want to simplify this expression. One way to simplify such an expression is to rationalize the denominator. To do this, we multiply both the numerator and denominator by \(\sqrt{7}\):

\[
\frac{1}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} = \frac{\sqrt{7}}{7}
\]

This gives the simplified form:

\[
\frac{\sqrt{7}}{7}
\]

Looking at the answer choices:

a) \(\frac{\sqrt{7}}{7}\)  
b) \(\frac{1}{\sqrt{49}}\)  
c) \(\frac{1}{7}\)  
d) \(7\)

The correct answer is **a) \(\frac{\sqrt{7}}{7}\)**.

Would you like more details on this solution or have any further questions?

Here are five related questions to practice:
1. How would you simplify \(\frac{1}{\sqrt{3}}\)?
2. What is \(\frac{\sqrt{2}}{2}\) simplified from \(\frac{1}{\sqrt{2}}\)?
3. How can you rationalize \(\frac{1}{\sqrt{11}}\)?
4. What happens if you multiply \(\frac{1}{\sqrt{x}}\) by \(\sqrt{x}\)?
5. How does rationalizing the denominator help in simplifying expressions?

**Tip:** Rationalizing the denominator means removing the square root from the denominator by multiplying both the numerator and denominator by the same square root.

Learn how to simplify 1/√7 by rationalizing the denominator. This step-by-step guide demonstrates multiplying both the numerator and denominator by √7 to obtain the simplified form. Suitable for students in Grades 9-10.

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