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Prove that the following number is irrational \((2-3 \sqrt{5})\)

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Prove that the following number is irrational \((2-3 \sqrt{5})\)
in Mathematics by Platinum (101k points) | 233 views

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\((2-3 \sqrt{5})\)
Let us assume that \((2-3 \sqrt{5})\) is rational.
subtract given numbers from 2 , considering 2 is rational number. as we know, difference of two rational numbers is rational
\(2-(2-3 \sqrt{5})\) is rational.
\(\Rightarrow 3 \sqrt{5}\) is rational
above result is possible if 3 is rational and \(\sqrt{5}\) is rational. Because, product of two rational numbers is rational.
but the fact is \(\sqrt{5}\) is an irrational.
Our assumption is wrong, and \((2-3 \sqrt{5})\) is irrational
by Platinum (101k points)

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