Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 631 · 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 19 odd numbers (1 + 3 + 5 + …)?
2. 2.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
3. 3.What is 81²? =
4. 4.How many whole numbers lie between 37² and 38²?
5. 5.How many whole numbers lie between 48² and 49²?
6. 6.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
7. 7.What is 80²? =
8. 8.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
9. 9.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
10. 10.What is √289? =
11. 11.How many whole numbers lie between 14² and 15²?
12. 12.What is √7744? =
13. 13.What is √1764? =
14. 14.What is the smallest whole number by which 216 must be divided to get a perfect square?
15. 15.What is the smallest whole number by which 1215 must be divided to get a perfect square?
16. 16.How many whole numbers lie between 33² and 34²?
17. 17.Which of these is a perfect square? (a) 900 (b) 907 (c) 911
18. 18.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
19. 19.What is √6400? =
20. 20.What is √625? =
21. 21.How many whole numbers lie between 23² and 24²?
22. 22.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
23. 23.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
24. 24.What is 83²? =
25. 25.How many whole numbers lie between 47² and 48²?
26. 26.What is √7569? =
27. 27.Which of these is a perfect square? (a) 225 (b) 252 (c) 228
28. 28.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
29. 29.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
30. 30.How many whole numbers lie between 9² and 10²?
31. 31.What is the smallest whole number by which 24 must be divided to get a perfect square?
32. 32.What is √576? =
33. 33.A square garden has an area of 3249 square m. How long is each side (in m)?
34. 34.What is √5476? =
35. 35.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
36. 36.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
37. 37.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
38. 38.Which of these is a perfect square? (a) 1369 (b) 1400 (c) 1390
39. 39.What is 42²? =
40. 40.What is √4761? =

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