Question

step bye step explanation to prove that √7 is irrational.​

Answer 1

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Let us assume that √7 be rational.

Then it must in the form of p / q [q ≠ 0] [p and q are co-prime]

$√7 = \frac{p}{q}$

$=> √7 x q = p$

Squaring on both sides

$=> 7q²= p²------ (1)$

p² is divisible by 7

p is divisible by 7

p = 7c [c is a positive integer] [squaring on both sides ]

p² = 49 c² --------- (2)

Subsitute p² in equ (1) we get

$7q² = 49 c²$

$q² = 7c²$

=> q is divisible by 7

Thus q and p have a common factor7.

There is a contradiction as our assumsion p & q are co prime but it has a common factor.

So that √7 is an irrational.