Question

prove that 4-5√2 is an irrational number.​

Answer 1

Answer:

Let us assume that (4−5

2

) is rational .

Subtract given number from 4, considering 4 is rational number. as we know difference of two rational numbers is rational.

4−(4−5

2

)is rational

⇒5

2

is rational

which is only possible if 5 is rational and

2

is rational.

As we know prouduct of two rational number s rational

But the fact is

2

is an irrational.

Which is contradictory to our assumption.

Hence, 4−5

2

is irrational . hence proved.

Answer 2

Answer:

Let 4-5√2 is a rational number so it can be expressed in the of p/q

4-5√2 = p/q

-5√2 q = 4p

√2 q = 4p+5

∆ 4-5√ 2 is an irrational number