Question

Prove that 3 root 2 minus 5 is a irrational number

Answer 1

To prove:
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3√2 - 5 is irrational
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Let us assume to contrary that 3√2-5 is rational .

i.e .we can find coprimes a and b (b not equal to 0) such that 3√2-5 =a/b

=》》3√2=a/b + 5

√2=(a+5b)/3b

Since a and b are integers ,a + 5b/3b is rational but thid contradict the fact that

√2 is irrational.So our assumption is wrong.

There fore ,

3√2-5 is irrational
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