Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 256 · 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 12 odd numbers (1 + 3 + 5 + …)?
2. 2.What is 96²? =
3. 3.What is the smallest whole number by which 360 must be divided to get a perfect square?
4. 4.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
5. 5.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
6. 6.What is √144? =
7. 7.What is √1296? =
8. 8.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
9. 9.What is the smallest whole number by which 686 must be divided to get a perfect square?
10. 10.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
11. 11.How many whole numbers lie between 9² and 10²?
12. 12.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
13. 13.A square garden has an area of 169 square m. How long is each side (in m)?
14. 14.What is √6561? =
15. 15.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
16. 16.What is 70²? =
17. 17.How many whole numbers lie between 31² and 32²?
18. 18.How many whole numbers lie between 39² and 40²?
19. 19.What is the smallest whole number by which 56 must be divided to get a perfect square?
20. 20.How many whole numbers lie between 43² and 44²?
21. 21.What is √1089? =
22. 22.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
23. 23.Which of these is a perfect square? (a) 1629 (b) 1600 (c) 1636
24. 24.How many whole numbers lie between 20² and 21²?
25. 25.What is 34²? =
26. 26.How many whole numbers lie between 10² and 11²?
27. 27.What is 97²? =
28. 28.A square garden has an area of 1225 square m. How long is each side (in m)?
29. 29.What is √9216? =
30. 30.What is 62²? =
31. 31.A square garden has an area of 361 square m. How long is each side (in m)?
32. 32.What is 48²? =
33. 33.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
34. 34.What is 92²? =
35. 35.A square garden has an area of 121 square m. How long is each side (in m)?
36. 36.What is √7744? =
37. 37.A square garden has an area of 2704 square m. How long is each side (in m)?
38. 38.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
39. 39.A square garden has an area of 1600 square m. How long is each side (in m)?
40. 40.What is √2809? =

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