Which number is an irrational number?2.56

Accepted Solution

Answer:[tex]-\sqrt{3}[/tex] is Irrational No.Step-by-step explanation:Irrational nos are no which can not be written in [tex]\frac{p}{q}[/tex] form and also decimal expansion of it is non terminating non repeating.Option 1: [tex]\sqrt{16}[/tex][tex]\sqrt{16} = \pm 4[/tex] and [tex]\pm 4[/tex] are rational nos.Thus, This is Rational No.Option 2: [tex]-\frac{22}{9}[/tex][tex]-\frac{22}{9}[/tex] , this is already in [tex]\frac{p}{q}[/tex] form.Thus, This is a Rational No.Option 3: [tex]-\sqrt{3}[/tex]Decimal expansion of [tex]\sqrt{3}[/tex] is non terminating non repeating⇒ Decimal expansion of [tex]-\sqrt{3}[/tex] is also non terminating non repeating.Thus, This is a irrational No.