Question

prove that root 5 is irrational​

Answer 1

Step-by-step explanation:

Let us assume ✓5 is rational number

Therefore ,

✓5=a/b, where AB are integers,b not equal to 0

Here a and b are co-prime

Therefore✓5b=a

square on both sides

(✓5b) square = (a) square

5b square = a square..........(1)

b square = a square\5

Therefore ,

5 divides a square

5 divides a

Let, a = 5c

put a =5c in (1)

5b square = (5c) square

5b square = 25c sqaure

b square = 5c square

5c square = b square

c square = b square/5

Therefore,

5 divides b square

5 divides b

Therefore,

A and B are not co-prime

Therefore,

Assumption become wrong

✓ 5 is a irrational number