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Question

Prove that (452) is an irrational number.

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Solution

Let us assume that (452) is rational .

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

4(452)is rational

52 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, 452 is irrational . hence proved.

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