Questions: Determine whether √30 is a whole number, integer, rational number and/or irrational number. [mark all correct answers] a. Whole b. Integer c. Rational d. Irrational

Solution Steps

• Whole numbers are non-negative integers (0, 1, 2, 3, ...).
• \(\sqrt{30}\) is approximately 5.477, which is not an integer.
• Therefore, \(\sqrt{30}\) is not a whole number.

• Integers include all whole numbers and their negatives (..., -2, -1, 0, 1, 2, ...).
• Since \(\sqrt{30}\) is not a whole number, it cannot be an integer.
• Therefore, \(\sqrt{30}\) is not an integer.

• A rational number can be expressed as a fraction \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b \neq 0\).
• \(\sqrt{30}\) cannot be expressed as a fraction of integers because 30 is not a perfect square.
• Therefore, \(\sqrt{30}\) is not a rational number.

• An irrational number cannot be expressed as a fraction of integers and has a non-terminating, non-repeating decimal expansion.
• Since \(\sqrt{30}\) is not a perfect square and cannot be expressed as a fraction, it is irrational.
• Therefore, \(\sqrt{30}\) is an irrational number.

Final Answer