Question

Q.1 Prove that under root 37 is an irrational number
$\sqrt{37}$
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Answer 1

Answer:Then it can be written in p/q form where q is not equal to zero. ... But p and q are co-prime. Hence,This contradicts our assumption. Therefore , √37 is irrational.

Step-by-step explanation: Let us assume√37 be rational number.

Then it can be written in p/q form where q is not equal to zero.

√37=p/q

√37 p=q

( Squaring both sides)

37p^2=q^2. { 1}

As 37p^2 is divisible by q^2

Therefore 37p is also divisible by q.

Let q be 37c where c is rational number.

q=37c

(Squaring both sides)

q^2 = 1369 c^2

As q^2 =37p^2 ( from 1)

37p^2=1369c^2

37c^2=p^2. (2)

37 is a factor of p^2

Therefore 37 is also a factor of p.

From 1 and 2 :

37 is common factor of p and q.

But p and q are co-prime.

Hence,This contradicts our assumption.

Therefore , √37 is irrational.

Hence Proved........

Thank u

Answer 2

Answer: If √37 is rational it should be written in the form of p/q where q is not equal to zero.

Here √37 cannot be written in the form p/q.

Hence it is irrational

THANK YOU

I HOPE IT HELPS