Question

Prove that root 2isirrational

Answer 1

Answer:

Assume that. root 2 is rational

Step-by-step explanation:

take a and b

root 2 equal to a / b

a and b are co prime nos.

squaring on both sides

u'll get

2 = a^2 /b^2

then 2b^2 = a^2

b square an d b is a multiple of 2 now

take an integer as c

a = 2c

substitute

2c^2 = 2b^2

4csquare

Answer 2

Answer:

Let √2 be a rational number.

A rational number can be written in the form of p/q.  

√2 = p/q  

p = √2q  

Squaring on both sides,  

p²=2q²  

2 divides p² then 2 also divides p.  

So, p is a multiple of 2.  

p = 2a (a is any integer)  

Put p=2a in p²=2q²  

(2a)² = 2q²  

4a² = 2q²  

2a² = q²  

2 divides q² then 2 also divides q.  

Therefore, q is also a multiple of 2.

So, q = 2b  Both p and q have 2 as a common factor.  

But this contradicts the fact that p and q are co primes.  

So our supposition is false.  

Therefore, √2 is an irrational number.

Hence proved.

Hope it helps

Step-by-step explanation:

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