Proof that √4 is irrational.(Proof this is wrong by not taking √4=2)Given : √4 is irrational number. Let √4 = a / b wher a,b are integers b ≠ 0 we also suppose that a / b is written in the simplest form Now √4 = a / b ⇒ 4 = a2 / b2 ⇒ 4b2 = a2 ∴ 4b2 is divisible by 2 ⇒ a2 is divisible by 2 ⇒ a is divisible by 2 ∴ let a = 4c a2 = 16c2 ⇒ 4b2 =16c2 ⇒ b2 = 4c2 ∴ 4c2 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 ∴ √4 is irrational number.
2. A number N when divided by 15 gives the remainder 4. What is the remainder when the same number is divided by 5 ?
Proof that √4 is irrational.(Proof this is wrong by not taking √4=2)
Given :
√4 is irrational number.
Let √4 = a / b wher a,b are integers b ≠ 0
we also suppose that a / b is written in the simplest form
Now √4 = a / b ⇒ 4 = a2 / b2 ⇒ 4b2 = a2
∴ 4b2 is divisible by 2
⇒ a2 is divisible by 2
⇒ a is divisible by 2
∴ let a = 4c
a2 = 16c2 ⇒ 4b2 =16c2 ⇒ b2 = 4c2
∴ 4c2 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
∴ √4 is irrational number.
77 × 42 × 37 × 57 × 30 × 90 × 70 × 2400 × 2402 × 243 × 343 is perfectly divisible by 21n
(A) 9 (B) 11 (C) 10 (D) 6