Question

Prove that 5-√3 is an irrational number.​

Answer 1

Let us assume that 5-root 3 is rational.

Then there exist co-primes a and b (b!=0) such that 5-root 3 =a/b

》root 3=a/b-5

》root 3=a-5b/b

Since a and b are integers, so a-2b/b is rational

Thus, root 3 is rational

But we know that root 3 is irrational

So,our assumption is incorrect.

Hence, 5-root 3 is irrational.

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