1. Which of these digits can a perfect square NEVER end with?
- A1
- B7
- C4
- D9
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Answer: B) 7
A perfect square can end only in 0, 1, 4, 5, 6 or 9. It can never end in 2, 3, 7 or 8. So 7 is impossible.
Class 8 Properties of Square Numbers — practice questions with answers
Squares and Roots · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. The sum of the first n odd natural numbers equals which square?
- An²
- B2n
- Cn(n+1)
- D(2n)²
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Answer: A) n²
1 + 3 + 5 + ... + (2n - 1) = n². This is a key property linking odd numbers to squares.
3. Between which two consecutive perfect squares does the number 50 lie?
- A49 and 64
- B36 and 49
- C25 and 49
- D64 and 81
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Answer: A) 49 and 64
49 = 7² and 64 = 8², and 49 < 50 < 64. So 50 lies between 7² and 8².
4. Dev wants the units digit of 123² without full multiplication.
He knows only the units digit matters.
What is the units digit of 123²?
He knows only the units digit matters.
What is the units digit of 123²?
- A18
- B10
- C8
- D9
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Answer: D) 9
The units digit of 123 is 3, and 3² = 9. So 123² ends in 9. (123² = 15129.)
5. Property challenge: The sum of the squares of the first n natural numbers is given by .
For n = 5, the squares are 1, 4, 9, 16, 25.
What is 1² + 2² + 3² + 4² + 5²?
For n = 5, the squares are 1, 4, 9, 16, 25.
What is 1² + 2² + 3² + 4² + 5²?
- A110
- B49
- C61
- D55
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Answer: D) 55
Using with n=5: . (Check: 1+4+9+16+25 = 55.)
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