Question

If p and q are co-prime numbers, then $p^{2} and q^{2}$ are
(a) coprime
(b) not coprime
(c) even
(d) odd

Answer 1

Answer:

Among the given options option (a) co-prime is  correct.  

Step-by-step explanation:

Given:  

p and q are co-prime numbers.

Two numbers are co-prime if their HCF is one (1)  i.e they have no  common factor other than 1.

Let us take an example :  

p = 3 and q = 5.

Factor of 3 = 1 , 3 & 5 = 1, 5

As 3 and 5 has no common factor other than 1, so p and q are co-prime.

Now p² = 3² = 9  and q2 = 25,

Factor of 9 = 1,3,9   & 25 = 1, 5 ,25

As 9 and 25 has no common factor other than 1,

So p² and q²  are also co-prime.

Hence, p² & q² are co-prime.

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Answer 2

Given: If p and q are co-prime numbers.

To find:  p2 and q2 are co primes.

Solution:

Two numbers are co-prime if their HCF is 1 i.e they have no number common other than 1.

Let us take p = 4 and q = 5.

As 4 and 5 has no common factor other than 1, p and q are co-prime.

Now p2 = 16 and q2 = 25,

As 16 and 25 has no common factor other than 1,

So p2 and q2 are also co-prime.