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.
This ICSE Class 8 Mathematics practice quiz has 44 multiple-choice questions on Squares and Square Roots, and 44 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.
Start quiz: 44 questions, freeSample questions
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
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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:
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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.
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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:
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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
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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.
More questions in this quiz
Answers and explanations are in the full quiz.
- Which of the following numbers is a perfect square? (A) 1024 (B) 1025 (C) 1026 (D) 1027
- The sum of the first 'n' odd natural numbers is equal to:
- If the area of a square is 225 cm^2, what is the length of its side?
- The square root of a number is 12. What is the number?
- What is the smallest number by which 180 must be multiplied to make it a perfect square?
- Which of the following is not a perfect square? (A) 441 (B) 529 (C) 676 (D) 781
- If sqrt(x) = 2.5, then x is:
- Which is the smallest number that must be subtracted from 3000 to make it a perfect square?
- The square root of 10.24 is:
- A number ending in 6 can be the square of a number ending in:
- Which of the following numbers is not a perfect square? (A) 1296 (B) 1369 (C) 1444 (D) 1522
- The square root of 0.0001 is:
- The number of zeros at the end of the square of a number can be:
- Which of the following is the square of an odd number? (A) 1234 (B) 5678 (C) 9876 (D) 8765
- The value of √144 + √121 is:
- If √625 = 25, then √6.25 is:
- What is the smallest number that must be added to 512 to make it a perfect square?
- The unit digit of (any number ending in 3)² is:
- If √49 = 7, then what is √0.0049?
- The smallest perfect square that is a multiple of both 4 and 9 is:
- The value of (√81 − √16) / √25 is:
- The number of perfect squares between 100 and 200 is:
- What is the side length of a square whose area is 64 square units?
- Which of the following numbers is the smallest perfect square divisible by 18?
- The square root of a number is approximately 5.3. What is the approximate value of the number?
- Which of the following is the smallest number that must be multiplied by 72 to make it a perfect square?
- The square root of a number ending in 0 will have a unit digit of:
- If √x = 1.1, then x is:
- The number of digits in the square root of a 6-digit number is:
- What is the smallest positive integer whose square is greater than 300?
- The value of √1296 is:
- What is the value of √(16/25) + √(9/16)?
- If √5329 = 73, then √53.29 is:
- The number of digits in the square root of a 7-digit number is:
- What is the least number that must be added to 1160 to make it a perfect square?
- If the square of a number is 49, what is the number?
- The sum of the squares of the first three odd natural numbers is:
- Which of the following numbers is a perfect square and ends with the digit 8?
- If the product of two consecutive natural numbers is 600, find the numbers.
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