Question

prove that 4-3✓2 is irrational

Answer 1

Let us assume that 4-3√2 is rational number.
So we can write 4-3√2 as a/b where a and b are co primes and b is not equal to 0.


4-3√2 = a/b.

-3√2 = a/b-4.

-3√2= a-4b/b

√2= a-4b/-3b


√2 = -a-4b/3b.

Here √2 is an irrational number.
But a-4b/-3b or -a-4b/3b is rational number.


Therefore it is a contradiction to our assumption that 4-3√2 is rational number.

Thus,4-3√2 is irrational number...




Hope this helps.

Answer 2

proof by contradiction:

let   4-3✓2 is rational
therfore
 4-3✓2 = a/b where a anf b are coprimes
 4-3✓2 = a/b
✓2 = (4-a/b)1/3
✓2  =(4b - a)/3b
here rhs is in the form of p/q
but we know that ✓2  is irrartional
therefore our assumption that 4-3✓2  is rational is wrong.
therefore 4-3✓2  is irrational
hence proved