Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 530 · 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 23 odd numbers (1 + 3 + 5 + …)?
3. 3.How many whole numbers lie between 11² and 12²?
4. 4.What is the smallest whole number by which 60 must be divided to get a perfect square?
5. 5.What is √1600? =
6. 6.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
7. 7.What is √2500? =
8. 8.What is 82²? =
9. 9.What is 24²? =
10. 10.What is 15²? =
11. 11.What is 28²? =
12. 12.What is √4624? =
13. 13.Which of these is a perfect square? (a) 1013 (b) 961 (c) 970
14. 14.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the smallest whole number by which 112 must be divided to get a perfect square?
16. 16.Which of these is a perfect square? (a) 960 (b) 938 (c) 900
17. 17.Which of these is a perfect square? (a) 1039 (b) 1079 (c) 1024
18. 18.Which of these is a perfect square? (a) 154 (b) 144 (c) 148
19. 19.What is √2809? =
20. 20.What is √7396? =
21. 21.What is 63²? =
22. 22.A square garden has an area of 225 square m. How long is each side (in m)?
23. 23.A square garden has an area of 2601 square m. How long is each side (in m)?
24. 24.What is √9801? =
25. 25.What is 43²? =
26. 26.Which of these is a perfect square? (a) 1636 (b) 1652 (c) 1600
27. 27.What is √361? =
28. 28.Which of these is a perfect square? (a) 121 (b) 135 (c) 143
29. 29.What is √256? =
30. 30.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
31. 31.How many whole numbers lie between 8² and 9²?
32. 32.A square garden has an area of 3600 square m. How long is each side (in m)?
33. 33.What is √2916? =
34. 34.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
35. 35.What is √196? =
36. 36.How many whole numbers lie between 43² and 44²?
37. 37.What is 40²? =
38. 38.What is 20²? =
39. 39.What is 78²? =
40. 40.How many whole numbers lie between 48² and 49²?

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