Question

Prove that √2 + √3 is an irrational number.
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Answer 1

Answer:

Let as assume that √2 + √3 is a rational number .

Then , there exists co - prime positive integers p and q such that

This contradicts the fact that √3 is irrational .

so assumption was incorrect . Here √2 + √3 is irrational.

Answer 2

√2 is an irrational number because it's decimal expansion is non terminating and non repeating.

√3 is also an irrational number same reason

√2 + √3 = (√2+√3)

They cannot be added because only like terms can be added.

Since both the numbers are irrational √2 + √3 is an irrational number.

Hence Proved.

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