Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 184 · 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 29 odd numbers (1 + 3 + 5 + …)?
2. 2.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
3. 3.What is 87²? =
4. 4.What is √289? =
5. 5.How many whole numbers lie between 31² and 32²?
6. 6.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
7. 7.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
8. 8.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
9. 9.How many whole numbers lie between 17² and 18²?
10. 10.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
11. 11.What is 17²? =
12. 12.A square garden has an area of 2116 square m. How long is each side (in m)?
13. 13.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
14. 14.What is √9604? =
15. 15.A square garden has an area of 3481 square m. How long is each side (in m)?
16. 16.What is 58²? =
17. 17.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
18. 18.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
19. 19.What is the smallest whole number by which 112 must be divided to get a perfect square?
20. 20.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
21. 21.What is √3600? =
22. 22.Which of these is a perfect square? (a) 256 (b) 259 (c) 272
23. 23.What is √4096? =
24. 24.Which of these is a perfect square? (a) 196 (b) 216 (c) 211
25. 25.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
26. 26.What is 52²? =
27. 27.What is 14²? =
28. 28.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
29. 29.How many whole numbers lie between 9² and 10²?
30. 30.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
31. 31.What is √6561? =
32. 32.What is 36²? =
33. 33.What is 45²? =
34. 34.A square garden has an area of 2809 square m. How long is each side (in m)?
35. 35.What is √1521? =
36. 36.Which of these is a perfect square? (a) 1376 (b) 1398 (c) 1369
37. 37.What is 38²? =
38. 38.Which of these is a perfect square? (a) 900 (b) 905 (c) 947
39. 39.What is √5329? =
40. 40.What is 63²? =

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