Question

Prove that 3-√7 is irrational number.

Answer 1

Step-by-step explanation:

assuming that 3-√7is a rational numbers

let a =3-√7

a-3=√7 -----(1)

a is rational and √7is a rational

from 1, rational =irrational no

so, 3-√7is a irrational number

Answer 2

Answer:

Let 3-root 7 is a rational number

i.e 3- root 7=p/q where p and q are co primes and q is not equal to 0

3-root 7=p/q

-root 7=p/q-3

-root 7=p-3q/q

root 7=-p+3q/q

But root 7 is an irrrational number and -p+3q/q is a rational no.

This means irrational no. is equal to rational no.

which is never possible.

Hence, it is a vo contradiction.

Our supposition is wrong.

Thus,3- root 7 is an irrational no.