- ASquare root of 2
- B−9
- C
- D0.75
Step-by-Step Solution
Square root of 2 cannot be written as p/q with integers p and q, so it is irrational. The others are all rational.
Answer: A) Square root of 2
Which of these numbers is NOT a rational number?
Class 7Rational NumbersRational Numbers
Key idea: Recognising rationals
If you can write a number as **integer over non-zero integer**, it is rational. So:
- All integers are rational: 5 = 5/1, 0 = 0/1, −9 = −9/1.
- All fractions with integer numerator and denominator are rational: 3/4, −2/7, 11/3.
- Any decimal that terminates or repeats is rational: 0.25 = 1/4, 0.333… = 1/3.
Numbers that cannot be written as p/q (like √2 or π) are NOT rational — they're irrational. You'll meet those in Class 9.
- All integers are rational: 5 = 5/1, 0 = 0/1, −9 = −9/1.
- All fractions with integer numerator and denominator are rational: 3/4, −2/7, 11/3.
- Any decimal that terminates or repeats is rational: 0.25 = 1/4, 0.333… = 1/3.
Numbers that cannot be written as p/q (like √2 or π) are NOT rational — they're irrational. You'll meet those in Class 9.
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