Question

Prove that 2 root 2 is an irrational number class 10

Answer 1

Answer:

it is Given √2 is irrational number. ∴p are q are divisible by 2 . ∴ √2 is irrational number.Apr 12, 2017

Answer 2

Step-by-step explanation:

We are going to prove it by contradiction.

First, let's assume 2√2 to be rational.

then,

2√2 = p/q, where q≠0 and p, q be co primes

then,

p = 2q√2. ( squaring on both sides)

p²=8q²

let's take 4q² as y² (because 4q²=(2q)²). *****(1)

then we get

p² = 2y²

here we see that p² is divisible by 2, so p is also

divisible by 2. .*****(2)

from (1) and (2), we see that both q and p are divisible

by 2. but this is contradicting that p, q are co primes

So, the assumption that 2√2 is rational is false.

hope it helps. if there are any corrections please inform me. (◠‿◕)