Question

Root 37 is an irrational number prove that

Answer 1

i hops it is clear to you..

plss brainliest my answer..

Answer 2

Answer:

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