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

If q is the square fo a natural number p, then p is

A

the square root of q

B

equal to q

C

greater than q

D

the square of q

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the relationship between \( p \) and \( q \) given that \( q \) is the square of a natural number \( p \). ### Step-by-Step Solution: 1. **Understanding the Given Information**: We are given that \( q \) is the square of a natural number \( p \). This can be mathematically expressed as: \[ q = p^2 \] 2. **Rearranging the Equation**: We need to find \( p \) in terms of \( q \). To do this, we can rearrange the equation: \[ p = \sqrt{q} \] 3. **Considering the Nature of \( p \)**: Since \( p \) is a natural number, we need to ensure that \( q \) is a perfect square. This is because the square root of a number is a natural number only if that number is a perfect square. 4. **Conclusion**: Thus, we conclude that if \( q \) is the square of a natural number \( p \), then \( p \) can be expressed as: \[ p = \sqrt{q} \] ### Final Answer: Therefore, \( p \) is the square root of \( q \). ---
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