Question

quest 21 and 22 please please please please​

Answer 1

hey mate here is your answer

21.√2 is an irrational number because its decimal expantion is 1.4142135.... which is a non-terminating and non- reccuring decimal.

22.√3is not a rational number because its decimal expantion is 1.732050807...which has the property of irrational numbers because it is non-terminating and non-reccuring.

hope it will help you

Answer 2

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.