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If q is the square of a natural number p...

If `q` is the square of a natural number `p`, then `p` is:

A

the square of `q`

B

the square root of `q`

C

equal to `q`

D

greater than `q`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to determine the value of \( p \) given that \( q \) is the square of a natural number \( p \). Let's go through the steps systematically. ### Step-by-Step Solution: 1. **Understanding the relationship**: We know from the problem that \( q \) is the square of a natural number \( p \). This can be mathematically expressed as: \[ q = p^2 \] 2. **Isolating \( p \)**: To find \( p \), we need to express it in terms of \( q \). We can do this by taking the square root of both sides of the equation: \[ p = \sqrt{q} \] 3. **Conclusion**: Since \( p \) is a natural number and \( q \) is the square of \( p \), \( \sqrt{q} \) must also yield a natural number. Therefore, we conclude: \[ p = \sqrt{q} \] ### Final Answer: Thus, the value of \( p \) is \( \sqrt{q} \). ---
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