Question

Prove that the following number is irrational:-
$\sqrt{7}$

Answer 1

hey friend here is your answer....
√7 is irrational because it value is 2.64575131 (approx)
which is a not terminating and non repeating....
that's why√7 is irrational...
hope it helps you dear friend...
if it helps mark as brainliest

Answer 2

prove that √7 is irrational

Let us assume √7 is rational

√7=p/q( where p and q are co- prime)

squaring on both sides

(√7)^2=p^2/q^2
7=p^2/q^2
7q^2=p^2
q^2=p^2/7

7 divides p and p^2 also

let p=7m

7q^2=(7m)^2
7q^2=49m
7q^2/49=m
q^2/7=m

7 divides q and q^2

our assumption is wrong
It is contradiction
Hence √7 is irrational

HENCE PROVED

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