Question

Prove that 5+2√3 irrational numbers

Answer 1

We have to prove that 5+2√3 is an irrational number.

So, let 5+2√3 be a rational number.

Therefore, it can be represented by p and q

i.e 5+2√3 = p/q (where p and q are integers, q is not equal to 0 and q and p are co-prime numbers)

2√3=p/q -5

2√3=p-5q/q

√3=p-5q/-2q

we know that p/q is a rational number,

but, √3 is an irrational number.

This contradicts our assumption, therefore 5+2√3 is an irrational number.

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