1.

Show that 2-root3 is irrational no​

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\large{\underline{\bf{\pink{Correct\:Question:-}}}}

prove that 2+ √3 is IRRATIONAL.

\large{\underline{\bf{\purple{To\:prove:-}}}}

  • ✦ 2 + √3 is irrational.

\huge{\underline{\bf{\red{Proof:-}}}}

Let us assume, that 2 + √3 is rational.

Then,

There EXIST CO - primes a and b (b≠ 0)

So,

➝ (2 + √3) = a/b

\mapsto \rm\:( 2+ \sqrt{3} ) = \frac{a}{b} \: \\ \\\mapsto \rm\: \sqrt{3} = \frac{a}{b} - 2 \\ \\ \mapsto \rm\: \sqrt{3} = \frac{a - 2b}{b} \\ \\ \rm\:since \: \bf \: a \rm\: and \: \bf \: b \rm \: are \: intigers \: \\ \rm \: so \:, \: \frac{a - 2b}{b} \: \: is \: rational. \\ \\ \rm \: so ,\: \sqrt{3} \: is \: also \: rational. \\\\

But , we know that √3 is irrational.

So, this contradiction is arissen because of our wrong assumption.

Hence, (2 + √3 ) is irrational.

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