Question

(root2-2)whole square 2 is a rational or irrational iwant full some and give the explanation please

Answer 1

Sol:
Given √2 is irrational number.
Let √2 = a / b wher a,b are integers b ≠ 0
we also suppose that a / b is written in the simplest form
Now √2 = a / b ⇒ 2 = a2 / b2 ⇒ 2b2 = a2
∴ 2b2 is divisible by 2
⇒ a2 is divisible by 2
⇒ a is divisible by 2
∴ let a = 2c
a2 = 4c2 ⇒ 2b2 = 4c2 ⇒ b2 = 2c2
∴ 2c2 is divisible by 2
∴ b2 is divisible by 2
∴ b is divisible by 2
∴a are b are divisible by 2 .
this contradicts our supposition that a/b is written in the simplest form
Hence our supposition is wrong
∴ √2 is irrational number.

Answer 2

Answer:

Irrational

Step-by-step explanation:

Applying [ (a-b)^2 ]

(root2  -2)^2= (root2)^2 -2*root2*2 +2^2

                    =2 - 4root2 +4

                    = 6 - 4root2

As a rational number - an irrational number is always an irrational number

Hence, (root2 -2)^2  irrational