Question

Prove that √3 is an irrational number.

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Answer 1

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Question :- Prove that √3 is an irrational number.

Solution:

Let to be √3 be Rational number

Let it's simplest form be a/b

then,

Here,

Note:-
a and b are Integer having no common factor other than 1.

Again,

√3=a/b

Now,

Squaring the both sides means (L.H.S and RHS)

we get,

(√3)²=(a/b)²

(3)=a²/b²

Here, using cross multiplication...

3b²=a²

Now,. 

3 Divide a²

Again,

3 Divide a

Note Reason:- 3 is a prime Number and 3 Divide by a² 

Now,

Let to be a=3c

then,

(3b²)=9c²

Note:- 9 divide by 3

b²=3c²

Again,

3 Divide by b²

3 Divide by a

Now,

3 is a common factor of a and b...

Thus,

√3 is an irrational number..

Conclusion :- √3 is an irrational number.

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Answer 2

Answer is on attachment ....


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