Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 620 · 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 smallest whole number by which 32 must be multiplied to get a perfect square?
2. 2.What is the smallest whole number by which 540 must be divided to get a perfect square?
3. 3.Which of these is a perfect square? (a) 569 (b) 572 (c) 529
4. 4.What is 75²? =
5. 5.How many whole numbers lie between 26² and 27²?
6. 6.What is 55²? =
7. 7.What is 51²? =
8. 8.Which of these is a perfect square? (a) 912 (b) 900 (c) 925
9. 9.A square garden has an area of 784 square m. How long is each side (in m)?
10. 10.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
11. 11.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
12. 12.What is 66²? =
13. 13.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
14. 14.A square garden has an area of 1024 square m. How long is each side (in m)?
15. 15.A square garden has an area of 961 square m. How long is each side (in m)?
16. 16.Which of these is a perfect square? (a) 617 (b) 589 (c) 576
17. 17.What is √9025? =
18. 18.A square garden has an area of 3600 square m. How long is each side (in m)?
19. 19.What is 54²? =
20. 20.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
21. 21.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
22. 22.Which of these is a perfect square? (a) 1335 (b) 1356 (c) 1296
23. 23.How many whole numbers lie between 49² and 50²?
24. 24.What is 79²? =
25. 25.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
26. 26.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
27. 27.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
28. 28.What is √4489? =
29. 29.A square garden has an area of 1369 square m. How long is each side (in m)?
30. 30.What is √4624? =
31. 31.What is the smallest whole number by which 224 must be divided to get a perfect square?
32. 32.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
33. 33.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
34. 34.What is 31²? =
35. 35.How many whole numbers lie between 31² and 32²?
36. 36.How many whole numbers lie between 34² and 35²?
37. 37.A square garden has an area of 49 square m. How long is each side (in m)?
38. 38.What is √1369? =
39. 39.How many whole numbers lie between 5² and 6²?
40. 40.What is the smallest whole number by which 567 must be multiplied to get a perfect square?

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