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To solve for \( x \) in the equation:

\[
7 \sqrt{x} = 1
\]

we'll go through the following steps:

1. **Isolate** the square root term by dividing both sides by 7:
   \[
   \sqrt{x} = \frac{1}{7}
   \]

2. **Square both sides** to eliminate the square root:
   \[
   x = \left(\frac{1}{7}\right)^2
   \]

3. Simplify the result:
   \[
   x = \frac{1}{49}
   \]

### Final Answer:
\[
x = \frac{1}{49}
\]

Would you like further explanation on any part of this solution?

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Here are some related questions you might find useful:
1. What if \( 7 \sqrt{x} = k \) where \( k \neq 1 \)? How would the solution change?
2. How would you solve \( 7 \sqrt{x} = -1 \)?
3. What happens if we have \( 7 \sqrt{x} = 0 \)?
4. How do you solve for \( x \) if the equation is \( 7 \sqrt{x} = x \)?
5. How does this approach change if \( \sqrt{x} \) were replaced with \( x^2 \) in the equation?

**Tip:** When dealing with square roots, isolating the root term first often simplifies the steps needed to solve for the variable.

Find the value of x given that 7√x = 1.

Learn how to solve for x in the equation 7√x = 1 with a detailed, step-by-step solution. This algebra problem demonstrates techniques for isolating square roots and solving equations. Suitable for students in Grades 7-9.

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