Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

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

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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.

Watch 3-min video & get full concept clarity