Question

Prove that sq.root p Is a prime no.
4 mark question

Answer 1

Answer:

If p is a prime number, then p–√p is irrational.

I know that this question has been asked but I just want to make sure that my method is clear. My method is as follows:

Let us assume that the square root of the prime number pp is rational. Hence we can write p–√=abp=ab. (In their lowest form.) Then p=a2b2p=a2b2, and so pb2=a2pb2=a2.

Hence pp divides a2a2, so pp divides aa. Substitute aa by pkpk. Find out that pp divides bb. Hence this is a contradiction as they should be relatively prime, i.e., gcd(a,b)=1(a,b)=1.

Answer 2

Answer:

√ 4 = 2

2 is a prime no .

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