Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 312 · 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 30 odd numbers (1 + 3 + 5 + …)?
2. 2.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
3. 3.A square garden has an area of 144 square m. How long is each side (in m)?
4. 4.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
5. 5.What is 96²? =
6. 6.A square garden has an area of 3600 square m. How long is each side (in m)?
7. 7.How many whole numbers lie between 28² and 29²?
8. 8.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
9. 9.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
10. 10.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
11. 11.Which of these is a perfect square? (a) 169 (b) 187 (c) 181
12. 12.What is 57²? =
13. 13.What is √196? =
14. 14.Which of these is a perfect square? (a) 1126 (b) 1123 (c) 1089
15. 15.What is √3025? =
16. 16.What is 73²? =
17. 17.What is √7056? =
18. 18.How many whole numbers lie between 14² and 15²?
19. 19.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
20. 20.What is 85²? =
21. 21.What is the smallest whole number by which 320 must be multiplied to get a perfect square?
22. 22.What is 20²? =
23. 23.A square garden has an area of 64 square m. How long is each side (in m)?
24. 24.Which of these is a perfect square? (a) 149 (b) 147 (c) 144
25. 25.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
26. 26.Which of these is a perfect square? (a) 1241 (b) 1225 (c) 1290
27. 27.What is the smallest whole number by which 468 must be divided to get a perfect square?
28. 28.What is √289? =
29. 29.What is 87²? =
30. 30.Which of these is a perfect square? (a) 1467 (b) 1495 (c) 1444
31. 31.Which of these is a perfect square? (a) 471 (b) 441 (c) 468
32. 32.What is √9409? =
33. 33.Which of these is a perfect square? (a) 1311 (b) 1296 (c) 1304
34. 34.What is the smallest whole number by which 343 must be divided to get a perfect square?
35. 35.How many whole numbers lie between 7² and 8²?
36. 36.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
37. 37.A square garden has an area of 400 square m. How long is each side (in m)?
38. 38.How many whole numbers lie between 42² and 43²?
39. 39.What is √2401? =
40. 40.What is √4761? =

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