Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 314 · 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 16 odd numbers (1 + 3 + 5 + …)?
2. 2.What is √7744? =
3. 3.What is 88²? =
4. 4.Which of these is a perfect square? (a) 1173 (b) 1156 (c) 1211
5. 5.What is 13²? =
6. 6.What is √3249? =
7. 7.Which of these is a perfect square? (a) 484 (b) 520 (c) 518
8. 8.How many whole numbers lie between 25² and 26²?
9. 9.What is √2809? =
10. 10.What is the smallest whole number by which 72 must be divided to get a perfect square?
11. 11.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
12. 12.What is √1296? =
13. 13.How many whole numbers lie between 31² and 32²?
14. 14.How many whole numbers lie between 9² and 10²?
15. 15.Which of these is a perfect square? (a) 603 (b) 576 (c) 591
16. 16.What is √7056? =
17. 17.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
18. 18.What is √7921? =
19. 19.What is 27²? =
20. 20.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
21. 21.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
22. 22.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
23. 23.What is √8836? =
24. 24.What is the smallest whole number by which 832 must be divided to get a perfect square?
25. 25.Which of these is a perfect square? (a) 960 (b) 900 (c) 944
26. 26.How many whole numbers lie between 37² and 38²?
27. 27.What is 63²? =
28. 28.A square garden has an area of 676 square m. How long is each side (in m)?
29. 29.What is the smallest whole number by which 18 must be divided to get a perfect square?
30. 30.What is √1936? =
31. 31.How many whole numbers lie between 18² and 19²?
32. 32.A square garden has an area of 169 square m. How long is each side (in m)?
33. 33.Which of these is a perfect square? (a) 245 (b) 225 (c) 255
34. 34.What is √2401? =
35. 35.What is 49²? =
36. 36.How many whole numbers lie between 34² and 35²?
37. 37.What is the smallest whole number by which 360 must be multiplied to get a perfect square?
38. 38.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
39. 39.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
40. 40.What is √3600? =

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