Question

(4+√3)³rationalisation​

Answer 1

Answer:

Let us assume the contrary, that 4−

3

is rational.

That is, we can find co-prime a and b (b



=0) such that 4−

3

=

b

a

.

Therefore 4−

b

a

=

3

.

Rearranging this equation, we get

3

=4−

b

a

=

b

4b−a

Since a and b are integers, we get

b

4b−a

is rational, and so

3

is rational.

But this contradicts the fact that

3

is irrational,

This contradicts the fact that

3

is irrational.

This contradiction has arisen because of our incorrect assumption that 4-

3

is rational.

so, we conclude that 4−

3

is irrational