Question

prove that it's irrational

Answer 1

let us assume that √7 is rational

then it will be in the form of p/q


√7=p/q

squaring on both sides

7=p²/ q

q²×7=p²--------------(1)

if 7 divides then 7 also divides p

p=7a

substitute in equation 1

q²×7=(7a) ²
q²=7a²

If 7 divides q² 7 also divides q

then 7 is the common factor of p and q

but it contradicts the fact that they are coprimes

so our assumption is wrong

so √7 is irrational

I hope it helps you

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