Select the correct answer.

Which number is an irrational number?

A. [tex]\sqrt{100}[/tex]
B. [tex]\frac{1}{8}[/tex]
C. -2.2675
D. [tex]\sqrt[3]{16}[/tex]



Answer :

Certainly! Let's examine each option step by step to determine which number is irrational.

Option A: [tex]\(\sqrt{100}\)[/tex]

The square root of 100 is:
[tex]\[ \sqrt{100} = 10 \][/tex]
10 is a whole number, which means it is rational. Therefore, [tex]\(\sqrt{100}\)[/tex] is not an irrational number.

Option B: [tex]\(\frac{1}{8}\)[/tex]

The fraction [tex]\(\frac{1}{8}\)[/tex] can be expressed as a decimal:
[tex]\[ \frac{1}{8} = 0.125 \][/tex]
Since 0.125 is a terminating decimal, it is rational. Therefore, [tex]\(\frac{1}{8}\)[/tex] is not an irrational number.

Option C: -2.2675

The number -2.2675 is a finite decimal, which can be expressed as a fraction:
[tex]\[ -2.2675 = -\frac{22675}{10000} \][/tex]
Since it can be expressed as a fraction, it is rational. Therefore, -2.2675 is not an irrational number.

Option D: [tex]\(\sqrt[3]{16}\)[/tex]

The cube root of 16 is not a whole number. Let's consider its properties:
[tex]\[ \sqrt[3]{16} \approx 2.5198421... \][/tex]
This value does not terminate or repeat, meaning it cannot be precisely expressed as a fraction. Therefore, [tex]\(\sqrt[3]{16}\)[/tex] is an irrational number.

After analyzing each option, we conclude that:

The correct answer is:

D. [tex]\(\sqrt[3]{16}\)[/tex]