Answer:
Option B is irrational
Step-by-step explanation:
Given 4 options, we have to choose the option which is an irrational number .
An irrational number is a number that can't be expressed as a fraction or in form of [tex]\frac{p}{q}[/tex] , where q≠0. They have decimal expansions that neither terminate nor become periodic i.e non-terminating non-repeating.
Option A: [tex]\frac{-22}{9}=-2.444...[/tex]
which is non-terminating but repeating
∴ can be expressed in form of [tex]\frac{p}{q}[/tex].
Hence, rational
Option B: [tex]-\sqrt3=-1.7320508...[/tex]
The above is non-repeating and non-terminating.
⇒ irrational number
Option 3: [tex]2.56=\frac{256}{100}[/tex]
shows can be expressed as a fraction or in form of [tex]\frac{p}{q}[/tex]
hence, rational.
Option 4: [tex]\sqrt16=\pm4[/tex]
shows can be expressed as a fraction or in form of [tex]\frac{p}{q}[/tex]
hence, rational number
Option B is irrational.
