Prove that 3 - 2√3 is an irrational number, if √3 is irrational
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To prove: 2 + 3 3 is irrational, let us assume that 2 + 3 3 is rational. 2 + 3 3 = a b ; b ≠ 0 and a and b are integers. Since a and b are integers so, a - 2 b will also be an integer. So, a - 2 b 3 b will be rational which means is also rational.
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A rational number can be written in the form of p/q. p,q are integers then (p-6q)/2q is a rational number. But this contradicts the fact that √3 is an irrational number. ... Therefore,3+2√3 is an irrational number.
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