Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 661 · 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 smallest whole number by which 637 must be divided to get a perfect square?
2. 2.What is 16²? =
3. 3.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
4. 4.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
5. 5.A square garden has an area of 324 square m. How long is each side (in m)?
6. 6.What is 31²? =
7. 7.What is √144? =
8. 8.What is 38²? =
9. 9.What is √2209? =
10. 10.A square garden has an area of 1849 square m. How long is each side (in m)?
11. 11.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
12. 12.What is √289? =
13. 13.A square garden has an area of 3136 square m. How long is each side (in m)?
14. 14.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
16. 16.Which of these is a perfect square? (a) 532 (b) 570 (c) 529
17. 17.Which of these is a perfect square? (a) 1401 (b) 1420 (c) 1369
18. 18.Which of these is a perfect square? (a) 922 (b) 900 (c) 935
19. 19.How many whole numbers lie between 10² and 11²?
20. 20.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
21. 21.What is √9025? =
22. 22.What is 56²? =
23. 23.Which of these is a perfect square? (a) 100 (b) 120 (c) 106
24. 24.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
25. 25.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
26. 26.What is the smallest whole number by which 735 must be divided to get a perfect square?
27. 27.What is 54²? =
28. 28.How many whole numbers lie between 13² and 14²?
29. 29.How many whole numbers lie between 27² and 28²?
30. 30.A square garden has an area of 3025 square m. How long is each side (in m)?
31. 31.How many whole numbers lie between 7² and 8²?
32. 32.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
33. 33.What is the smallest whole number by which 128 must be divided to get a perfect square?
34. 34.What is √3721? =
35. 35.Which of these is a perfect square? (a) 625 (b) 631 (c) 663
36. 36.What is 17²? =
37. 37.What is the smallest whole number by which 54 must be divided to get a perfect square?
38. 38.What is √3025? =
39. 39.What is the smallest whole number by which 405 must be divided to get a perfect square?
40. 40.What is √6084? =

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