Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 179 · 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 540 must be divided to get a perfect square?
2. 2.What is √784? =
3. 3.What is √1225? =
4. 4.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
5. 5.What is 44²? =
6. 6.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
7. 7.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
8. 8.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
9. 9.What is 24²? =
10. 10.Which of these is a perfect square? (a) 574 (b) 529 (c) 537
11. 11.What is 69²? =
12. 12.Which of these is a perfect square? (a) 441 (b) 447 (c) 445
13. 13.Which of these is a perfect square? (a) 948 (b) 900 (c) 932
14. 14.What is 75²? =
15. 15.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
16. 16.What is √3025? =
17. 17.What is 36²? =
18. 18.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
19. 19.A square garden has an area of 3364 square m. How long is each side (in m)?
20. 20.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
21. 21.What is √9604? =
22. 22.How many whole numbers lie between 34² and 35²?
23. 23.A square garden has an area of 3136 square m. How long is each side (in m)?
24. 24.A square garden has an area of 1369 square m. How long is each side (in m)?
25. 25.How many whole numbers lie between 44² and 45²?
26. 26.What is √7056? =
27. 27.A square garden has an area of 400 square m. How long is each side (in m)?
28. 28.What is the smallest whole number by which 252 must be divided to get a perfect square?
29. 29.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
30. 30.What is 62²? =
31. 31.What is 71²? =
32. 32.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
33. 33.What is 98²? =
34. 34.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
35. 35.How many whole numbers lie between 16² and 17²?
36. 36.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
37. 37.What is 42²? =
38. 38.Which of these is a perfect square? (a) 1412 (b) 1369 (c) 1413
39. 39.What is the smallest whole number by which 135 must be divided to get a perfect square?
40. 40.What is √3969? =

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