Question

select the correct answer.

which number is an irrational number?

\\(\sqrt{100}\\)

\\(\frac{1}{8}\\)

-2.2675

\\(\sqrt3{16}\\)

Explanation:

Define rational and irrational numbers

Using the Rational Numbers and Irrational Numbers knowledge points

• A rational number can be written as a fraction \(\frac{a}{b}\) where \(a, b\) are integers and \(b

eq 0\).

• An irrational number cannot be expressed as a simple fraction, having non-terminating, non-repeating decimals.

Evaluate the first option

Using the Perfect Squares and Rational Numbers knowledge points

$$ \sqrt{100} = 10 = \frac{10}{1} $$

This is rational.

Evaluate the second and third options

Using the Rational Numbers knowledge point

• \(\frac{1}{8}\) is a ratio of two integers, so it is rational.
• \(-2.2675\) is a terminating decimal, which can be written as \(\frac{-22675}{10000}\), so it is rational.

Evaluate the fourth option

Using the Irrational Numbers knowledge point

• \(\sqrt[3]{16}\) is the cube root of \(16\).
• Since \(16\) is not a perfect cube, its cube root is non-terminating and non-repeating.
• Therefore, \(\sqrt[3]{16}\) is irrational.

Answer:

• (A) \(\sqrt{100}\)
• (B) \(\frac{1}{8}\)
• (C) \(-2.2675\)
• (D) \(\sqrt[3]{16}\) (Correct answer)