Question

Prove that  √7 is an irrational by proof of contadictio?

Answer 1

let us assume that √7 is a rational number ..
√7=p/q
aquaring both the side ..
(√7)^2=(p/q)^2
we will get 7 = p2/q2..

solve the equation till the end ..
your calculation will be wrong ..
then write that our asaumption is wrong so √7 is an irrarational no.

the #RIHAAN
hope this will help you.

Answer 2

Let √7 be a rational number.
A rational number can be written in the form of p/q where p,q are co primes
√7 = p/q
√7q = p
Squarinbg on both sides,
7q² = p² ---(1)
7 divides p² then 7 also divides p.
p has a factor 7.
Let p = 7a

Put p = 7a in eq (1)
7q² = (7a)²
7q2 = 49a²
q² = 7a²
7 divides q² then 7 also divides q.
q has a factor 7.

Both p and q have 7 as their common factor.
But this contradicts the fact that p and q are coprimes.
So our supposition is false.

Therefore, √7 is an irrational number.
Hence proved