Question

Prove that √5 is irrational​

Answer 1

given :- √5

√5 = p/q (q ≠ 0, p and q are coprime)

➡ √5q = p

squaring both sides,

➡ (√5q)² = (p)²

➡ 5q² = p² ----------(i)

therefore 5 divides p ---------(ii)

➡ 5 × r = p

again squaring both sides,

➡ (5 × r)² = (p)²

➡ 25 × r² = p²

➡ 25 × r² = 5q² (from equation (i)

➡ 5 × r² = q²

5 divides q², therefore 5 divides q ---------(iii)

from (ii) and (iii), we can say that p and q have common factor 5 which contradicts our assumption that p and q are coprime.

hence, our assumption is wrong and it's proved √5 is irrational.

Answer 2

Answer:

let √5 is rational

√5=a/b (a and b is co prime number and integers)

squaring both side

5=a square / b square

5b square =a square

5 divides b

so

let a =2c

2b square=2c square

2b square =4c square

b square =2c square

2 divides b

2 divides a and b

a and b are not coprime so our assumption is wrong

so

√5 is irrational

PLZ MARK AS BRAINLIST