Question

Prove that cube root of 2 is an irrational numbers

Answer 1

use cubrt(2) to mean cube root of 2
Let cubrt(2) = a/b which is in simplest form (no common factors except 1)
Then 2 = (a^3)/(b^3)
then 2(b^3) = a^3
This means a^3 is even. This means a is even.
Let a = 2k. So a^3 = 8k^3
This means 2(b^3) = 8k^3
then b^3 = 4k^3
This means b^3 is even. This means b is even
This implies both a and b are even.
But this is impossible because a/b is in simplest form
Therefore cubrt(2) is irrational
I hope this help you

Answer 2

Step-by-step explanation:

2=(a^3)/(b^3)

then 2*b^3)=a^3

means a^3iseven

a=2k

so.b^3=4k^3

means b^3 is even

then b is even

it mean a and b both are even

it is not possible because a and b is in simplest form

proved ube root 2 is irrational

hope u understand.