Question

Show that 2+ V3 is an Irrational number.​

Answer 1

$\huge\pink{\mid{\underline{\overline{\tt HELLO}}\mid}}$

$let \: \: 2 + \sqrt{3} \: be \: rational$

So,

$2 + \sqrt{3} =p \div q$

$\sqrt{3 } =(p \div q) - (2 \div 1)$

As RHS is is rational and LHS is irrational.

Our PREASSUMPTION I CONTRADICTED.

So...

$2 + \sqrt{3} \: is \: irrational$

HOPE IT HELPS UHH #CHEERS

Answer 2

Solution:-

Let ( 2 + √3 ) is an Rational Number.

∴ ( 2 + √3 ) can be written in the form of p/q.

=) ( 2 + √3 ) = p/q

=) √3 = p/q - 2

=) √3 = ( p - 2q)/q

Here,

p and q are some integers.

=) [( p - 2q)/q ] is an Rational Number but we know that √3 is an Irrational Number.

Rational Number can never be equal to Irrational Number.

∴ [( p - 2q)/q ] is an Irrational Number.

This Contradicts our supposition that ( 2 + √3 ) is a Rational Number.

Hence,

( 2 + √3 ) is an Irrational Number.