If p and q Are Coprime, Are p² and q² Also Coprime?

Video Explanation

Watch the video below for a clear explanation:

Solution

Question: If p and q are co-prime numbers, then p² and q² are:

(a) coprime    (b) not coprime    (c) even    (d) odd

Key Concept

Two numbers are called coprime if their HCF is 1.

If p and q are coprime, then:

HCF(p, q) = 1

Step 1: Consider Their Squares

p² and q² have the same prime factors as p and q respectively, only with doubled powers.

Step 2: Find the HCF

Since p and q have no common prime factor, their squares also have no common prime factor.

∴ HCF(p², q²) = 1

Final Answer

✔ p² and q² are coprime.

✔ Correct option: (a) coprime

Conclusion

Thus, the squares of two coprime numbers are also coprime.