Question

Show that 4-3root3 is an irrational number

Answer 1

Answer:

Step-by-step explanation:

Let us assume that 4 - 3√3 is rational.

∴ 4 - 3√3 = a/b   where a and b are co prime

4 - a/b = 3√3

4b -a/b = 3√3

4b - a/ 3b =√3

Now,

4b - a/ 3b is a rational number.

∴√3 is also rational.

This contradicts that  √3 is irrational.

This was due our wrong assumption.

∴ 4 - 3√3 is an irrational number.

Hence Proved