√7 ko Sankhya rekha per pradarshit kijiye
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follow the graphic methods
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Step-by-step explanation:
- Let us assume that √7 is a rational number.
- Then it must in the form of p/q [ ∵ q≠0]
- {p and q are co-prime number}
- √7=p/q
- squaring both sides
- 7 q^2=p^2 --------------------(1)
- p^2 is divisible by 7
- p is divisible by 7
- p=7 c [∵ c is a positive integer] {squaring both sides}
p^2 = 49 c^2-------------------(2)
substitute p^2 in equation (1) we get,
7 q^2=49 c^2
∴ Thus, q and p have a common factor of 7.
There is a contradiction.
As our assumption p and q are a co-prime
∵ But it has a common factor.
∴ So, that √7 is an irrational number.
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