Which of these numbers is neither Rational nor Integer?

Correct — C. Check each number against two definitions.

Integer: a whole number, positive, negative or zero.
Rational: expressible as p⁄q, with p and q integers and q ≠ 0.

√2 lies between 1 and 2 (1² = 1, 2² = 4), so it is not an integer.
√2 cannot be written as p⁄q, so it is not rational.
Neither label fits → option (c)

Why the others are wrong

• (a)
  −4 — −4 is an integer, since negative whole numbers count, and every integer is rational: −4 = −4⁄1. It is both, not neither.
• (b)
  1.5 — 1.5 = 3⁄2, a ratio of two integers, so it is rational. It is not an integer, but the question wants a number that is neither.
• (d)
  7 — 7 is an integer, and 7 = 7⁄1 makes it rational as well. It carries both labels the question rules out.

Real numbers split into rational numbers (a p⁄q form with q ≠ 0 exists) and irrational numbers (no such form). Integers sit wholly inside the rationals, because any integer n equals n⁄1.

So a number that is neither rational nor integer is simply an irrational number. The 'nor Integer' clause adds nothing, since no irrational number is an integer.

The square root of a whole number that is not a perfect square, such as √2, √3 or √7, is irrational. √4 = 2 and √9 = 3 are not.

Key facts

• Every integer is rational, because n = n⁄1.
• A terminating decimal such as 1.5 = 3⁄2 is rational, and so is a recurring decimal such as 0.333… = 1⁄3.
• The square root of a positive integer is either a whole number or irrational.
• Rational and irrational numbers together make up the real numbers.

Common traps

• Picking 1.5 because it is not an integer, and missing that 'neither' also needs it to be irrational.
• Treating integers and rationals as separate groups, when −4 and 7 belong to both at once.

No directly related past PYQ was found.