Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 413 · 40 sums

The method (Pairs make squares): Square: n × n. Quick way: (a + b)² = a² + 2ab + b², e.g. 42² = 1600 + 160 + 4. Square root: the number that times itself gives the square; a square ending in 4 has a root ending in 2 or 8. Make a perfect square: break into primes; multiply (or divide) by the prime left without a partner. 1 + 3 + 5 + … (n odd numbers) = n². Between n² and (n + 1)² there are 2n whole numbers.

1. 1.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
2. 2.What is the smallest whole number by which 810 must be divided to get a perfect square?
3. 3.What is √8281? =
4. 4.What is 86²? =
5. 5.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
6. 6.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
7. 7.What is the smallest whole number by which 27 must be divided to get a perfect square?
8. 8.What is √2809? =
9. 9.What is √4761? =
10. 10.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
11. 11.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
12. 12.Which of these is a perfect square? (a) 484 (b) 514 (c) 526
13. 13.What is √4900? =
14. 14.Which of these is a perfect square? (a) 900 (b) 920 (c) 956
15. 15.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
16. 16.How many whole numbers lie between 33² and 34²?
17. 17.What is √8649? =
18. 18.Which of these is a perfect square? (a) 803 (b) 835 (c) 784
19. 19.A square garden has an area of 25 square m. How long is each side (in m)?
20. 20.Which of these is a perfect square? (a) 1600 (b) 1632 (c) 1604
21. 21.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
22. 22.What is √1936? =
23. 23.Which of these is a perfect square? (a) 676 (b) 720 (c) 706
24. 24.What is 75²? =
25. 25.What is 84²? =
26. 26.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
27. 27.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
28. 28.A square garden has an area of 441 square m. How long is each side (in m)?
29. 29.What is 17²? =
30. 30.A square garden has an area of 2704 square m. How long is each side (in m)?
31. 31.Which of these is a perfect square? (a) 430 (b) 400 (c) 419
32. 32.How many whole numbers lie between 5² and 6²?
33. 33.Which of these is a perfect square? (a) 219 (b) 212 (c) 196
34. 34.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
35. 35.What is √7921? =
36. 36.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
37. 37.How many whole numbers lie between 12² and 13²?
38. 38.What is √676? =
39. 39.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
40. 40.What is 27²? =

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