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State true or false:
If p and q are co-prime numbers, then $p^{2}$ and $q^{2}$ are co-prime.

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True

False

answer is A.

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Detailed Solution

We have to check whether

p^{2}

and

q^{2}

are co-prime if p and q are co-prime numbers.
That means if a and b are co-prime. Then,

HCF (a, b) = 1

HCF (a^{2}, b^{2}) = HCF (a, b)

As co-prime numbers have only 1 as a common factor, p and q have no common factors other than 1.

\Rightarrow HCF (p, q) = 1

\Rightarrow HCF (p^{2}, q^{2}) = 1

So,

p^{2}

and

q^{2}

have no common factors other than 1.
That means

p^{2}

and

q^{2}

are co-prime.
Therefore, it is true that if p and q are co-prime numbers, then

p^{2}

and

q^{2}

are co-prime.
Hence, option 1 is correct.

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