Question

prove that 4-5underoot 2 is an irrational number

Answer 1

4-5√2 =a/b (assuming that it is rational).

5√2=4-a/b

√2 =4/5-a/5b.

here a, b are rational by assuption.

But this contradicts the fact that √2 was irrational.

so, 4-5√2 is irrational.

hope it helps you..