Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 119 · 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.Which of these is a perfect square? (a) 245 (b) 225 (c) 228
2. 2.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
3. 3.What is 31²? =
4. 4.What is √8836? =
5. 5.What is 84²? =
6. 6.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
7. 7.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
8. 8.A square garden has an area of 1369 square m. How long is each side (in m)?
9. 9.What is 70²? =
10. 10.What is √961? =
11. 11.What is √2916? =
12. 12.What is √5184? =
13. 13.A square garden has an area of 400 square m. How long is each side (in m)?
14. 14.What is 83²? =
15. 15.What is 26²? =
16. 16.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
17. 17.What is the smallest whole number by which 44 must be divided to get a perfect square?
18. 18.What is √5776? =
19. 19.What is 44²? =
20. 20.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
21. 21.Which of these is a perfect square? (a) 410 (b) 421 (c) 400
22. 22.What is 72²? =
23. 23.What is 36²? =
24. 24.What is the smallest whole number by which 486 must be divided to get a perfect square?
25. 25.A square garden has an area of 900 square m. How long is each side (in m)?
26. 26.What is 94²? =
27. 27.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
28. 28.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
29. 29.What is the smallest whole number by which 735 must be divided to get a perfect square?
30. 30.What is 16²? =
31. 31.What is √9801? =
32. 32.What is the smallest whole number by which 52 must be divided to get a perfect square?
33. 33.How many whole numbers lie between 20² and 21²?
34. 34.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
35. 35.What is √7396? =
36. 36.A square garden has an area of 169 square m. How long is each side (in m)?
37. 37.Which of these is a perfect square? (a) 364 (b) 386 (c) 361
38. 38.How many whole numbers lie between 21² and 22²?
39. 39.What is √8281? =
40. 40.What is √3025? =

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