AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

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

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

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

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

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

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!