Question

prove that √3 is an irrational number ​

Answer 1

Let us assume that root 3 is rational.

Root 3 = a/b where a and b are integers and coprimes.

Root 3 * b = a

Square LHS and RHS

3b2 = a2

b2 = a2/3

Therefore 3 divides a2 and 3 divides a.

Now take ,

a = 3c

Square ,

a2 = 9c2

3b2 = 9c2

b2/3 = c2

Therefore 3 divides b2 and b.

Answer 2

Answer:

below

Step-by-step explanation:

lets.do it through assumption method

lets consider root 3 as rational

thus

root 3=a/b

3=a^2/b^2 squring on both sides

3×b^2=a^2

now a divides 3 in a number

thus a=3c

apply in equation

3×b^2=3c^2

3×b^2=9c^2

b^2=3c^2

through this we cansay both are multiples of 3

this contradicts the fact that a and b are co primes

hence our assumption was wrong