Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 259 · 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 30²? =
2. 2.What is √7744? =
3. 3.What is √1296? =
4. 4.What is √2916? =
5. 5.Which of these is a perfect square? (a) 549 (b) 568 (c) 529
6. 6.Which of these is a perfect square? (a) 609 (b) 576 (c) 601
7. 7.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
8. 8.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
9. 9.What is 13²? =
10. 10.Which of these is a perfect square? (a) 769 (b) 751 (c) 729
11. 11.A square garden has an area of 2304 square m. How long is each side (in m)?
12. 12.Which of these is a perfect square? (a) 663 (b) 628 (c) 625
13. 13.How many whole numbers lie between 28² and 29²?
14. 14.How many whole numbers lie between 19² and 20²?
15. 15.What is 17²? =
16. 16.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
17. 17.What is √576? =
18. 18.A square garden has an area of 2601 square m. How long is each side (in m)?
19. 19.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
20. 20.What is √3600? =
21. 21.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
22. 22.How many whole numbers lie between 44² and 45²?
23. 23.What is the smallest whole number by which 448 must be divided to get a perfect square?
24. 24.Which of these is a perfect square? (a) 336 (b) 339 (c) 324
25. 25.How many whole numbers lie between 16² and 17²?
26. 26.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
27. 27.What is √625? =
28. 28.What is 50²? =
29. 29.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
30. 30.Which of these is a perfect square? (a) 289 (b) 296 (c) 322
31. 31.What is 67²? =
32. 32.How many whole numbers lie between 38² and 39²?
33. 33.How many whole numbers lie between 17² and 18²?
34. 34.Which of these is a perfect square? (a) 430 (b) 400 (c) 406
35. 35.Which of these is a perfect square? (a) 1521 (b) 1527 (c) 1592
36. 36.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
37. 37.What is √1369? =
38. 38.Which of these is a perfect square? (a) 384 (b) 367 (c) 361
39. 39.What is the smallest whole number by which 125 must be divided to get a perfect square?
40. 40.What is 81²? =

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