Question

prove that under root 2 is not a rational number​

Answer 1

Answer:

Proof that the square root of 2 is irrational. Assume is rational, i.e. it can be expressed as a rational fraction of the form , where and are two relatively prime integers. ... However, two even numbers cannot be relatively prime, so cannot be expressed as a rational fraction; hence is irrational.

Answer 2

$<I>$☞HEYA MATE ☜

★ Let us assume to the contray , that √2 is rational

→ The integers are r and s (≠0) such that √2=r/s

→ suppose r and s have common factor other than 1 , then we divide by the common factors other than 1 , to get √2=a/b , where a and b are co - primes .

→ So ,

√2b = a

√2b = a [squaring on both sides]

a² = 2b²

→ by the fundamental theorem of arthematic 2 divides a² then 2 divides a also .

→ Here we can write

a = 2c

a = 2c[squaring on both sides]

a² = 4c²

2b² = 4c²

b² = 2c²

2 divides b² then 2 divides b also

→ By this contradiction has arisen because of our assumption √2 is rational

♠ WE CONCLUDE THAT √2 IS IRRATIONAL NUMBER .

❣️Hope it helps uh ❣️