1.

Prove that (4 – 5√2 ) is an irrational number.

Answer»

Let us assume that (4 – 5√2 ) is a rational.

Subtract given number form 4, considering 4 is a rational number.

As we know, Difference of two rational numbers is a 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, product of two rational number is rational.

But the fact is √2 is an irrational.

Which is contradict to our assumption.

Hence, 4 – 5√2 is irrational. Hence Proved.



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