Question

Prove that 4 − 5√2 is an irrational number given that √2 is irrational.​

Answer 1

Prove that (4−5

2

) is an irrational number.

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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.

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