Question

✓2+✓3 is irrational. proove it

Answer 1

Hi friend,

Here is your answer,
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Let √2 + √3 = a/b where a/b is a rational number.

√2 + √3 = a/b
(√2 + √3)² = a²/b²                         {Squaring both sides}
2 + 3 + 2√6 = a²/b²
5 + 2√6 = a²/b²
2√6 = (a²/b²)-5

a,b and 5 are rational numbers.
So, 2√6 is also rational number.
This contradicts the fact that √6 is irrational.
Therefore √2 + √3 is irrational.
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