Squares and Square Roots Quiz - ICSE Class 8 Mathematics
Free practice quiz: Squares and Square Roots (ICSE Class 8 Mathematics). 44 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
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The square of a rational number can be: (A) a prime number (B) a negative number (C) a non-terminating decimal (D) a terminating decimal
- A only
- B only
- C only
- D only
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Answer: D. D only
The square of a rational number (p/q) is (p^2)/(q^2). If the denominator q, when expressed in its prime factorization, contains only primes 2 and 5, then the decimal representation of the rational number will terminate. For example, (3/4)^2 = 9/16, which terminates. The square of a rational number cannot be a prime number (unless it's 1, but 1 is not prime) or a negative number. It can be a non-terminating decimal if the original rational number's denominator has prime factors other than 2 and 5.
The unit digit of the square of 345 is:
- 0
- 1
- 5
- 6
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Answer: C. 5
To find the unit digit of the square of a number, we only need to consider the unit digit of the number itself. The unit digit of 345 is 5. The square of 5 is 25. The unit digit of 25 is 5. Therefore, the unit digit of the square of 345 is 5.
Which of the following statements is true? (A) The square root of every number is a whole number. (B) The square of a prime number is always a prime number. (C) Every number ending in 9 is a perfect square. (D) The square of a rational number is a rational number.
- A
- B
- C
- D
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Answer: D. D
(A) False. For example, sqrt(2) is not a whole number. (B) False. The square of a prime number (except 1, which is not prime) is composite. For example, 3 is prime, 3^2 = 9, which is not prime. (C) False. For example, 19 ends in 9 but is not a perfect square. (D) True. If a rational number is p/q, its square is (p/q)^2 = (p^2)/(q^2). Since p and q are integers, p^2 and q^2 are also integers, making (p^2)/(q^2) a rational number.
The unit digit of the square of a number ending in 7 is:
- 7
- 9
- 4
- 0
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Answer: B. 9
To determine the unit digit of the square of a number, we only need to consider the unit digit of the number itself. If a number ends in 7, its square will have a unit digit determined by 7 * 7. 7 * 7 = 49. The unit digit of 49 is 9. Therefore, the unit digit of the square of any number ending in 7 is 9.
If a number has 3 digits, its square will have: (A) 5 or 6 digits (B) 6 or 7 digits (C) 5 or 7 digits (D) 6 or 8 digits
- A
- B
- C
- D
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Answer: A. A
Let N be a 3-digit number. This means 100 ≤ N ≤ 999. Let S be the square of N, so S = N^2. The smallest 3-digit number is 100. 100² = 10000. This has 5 digits. The largest 3-digit number is 999. 999² = (1000 − 1)² = 1000000 − 2000 + 1 = 998001. This has 6 digits. Therefore, the square of a 3-digit number will have either 5 or 6 digits.