show 4 √2 is an irrational number
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Answered by
30
Heres your Answer
4√2 is irrational because it Cannot be written in p/q form where q is not equals to 0...
Hope it helps!
4√2 is irrational because it Cannot be written in p/q form where q is not equals to 0...
Hope it helps!
masumshaikh:
thanks for the help
np
Answered by
31
4√2 = √(16×2)
= √32
= 5.65....
therefore it's irrational number
but actual answer is
assume that √32 is an rational number
it is in the form of p/q where p and q are co primes
taking square on both sides
(√32)^2 = (p/q)^ 2
therefore
32 = p^2/q^2
p^2 = 32 q^2
therefore P is a multiple of 32
p = 32×k(constant)
32q^2 = (32k^2)
32q^2 = 1024k^2
q^2 = 32k^2
therefore Q is multiple of 32
the four p and q have common factor
therefore assumption is wrong
√32 = 4√2 is an irrational number
= √32
= 5.65....
therefore it's irrational number
but actual answer is
assume that √32 is an rational number
it is in the form of p/q where p and q are co primes
taking square on both sides
(√32)^2 = (p/q)^ 2
therefore
32 = p^2/q^2
p^2 = 32 q^2
therefore P is a multiple of 32
p = 32×k(constant)
32q^2 = (32k^2)
32q^2 = 1024k^2
q^2 = 32k^2
therefore Q is multiple of 32
the four p and q have common factor
therefore assumption is wrong
√32 = 4√2 is an irrational number
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