Question

prove that underoot 2 is irrational number​

Answer 1

Answer:

underoot 2 does not be showed as p over q so it is irrational number

Answer 2

Answer:

Let root 2 be a rational number

root 2 = p/q -- Eq 1

Squaring both sides of 1

2 = p2/q2

2q2 = p2 -- Eq 2 _

-> 2 divides p2 2/p\a

-> 2 divides p also -- Eq 3 |

0

From Euclids Division Lemma

p = 2a -- Eq 4

Put the value of p from Eq 4 in Eq 2

p2 = 2q2

(2a)2 = 2q2

4a2 = 2q2

2a2 = q2

-> 2 divides q2

-> 2 divides q also -- Eq 5

From Eq 3 and 5, 2 divides p and q

Therfore, Our supposition is wrong

Therefore, root 2 is an irrational number

Hope it helps☺