Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 689 · 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.A square garden has an area of 784 square m. How long is each side (in m)?
2. 2.What is √289? =
3. 3.What is 91²? =
4. 4.What is √961? =
5. 5.A square garden has an area of 225 square m. How long is each side (in m)?
6. 6.How many whole numbers lie between 15² and 16²?
7. 7.Which of these is a perfect square? (a) 303 (b) 289 (c) 309
8. 8.What is 68²? =
9. 9.What is √6561? =
10. 10.Which of these is a perfect square? (a) 171 (b) 179 (c) 169
11. 11.What is √484? =
12. 12.What is √4356? =
13. 13.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
14. 14.What is √2601? =
15. 15.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
16. 16.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
17. 17.Which of these is a perfect square? (a) 145 (b) 166 (c) 144
18. 18.What is 17²? =
19. 19.What is 21²? =
20. 20.A square garden has an area of 1521 square m. How long is each side (in m)?
21. 21.What is the smallest whole number by which 250 must be divided to get a perfect square?
22. 22.What is the smallest whole number by which 243 must be divided to get a perfect square?
23. 23.A square garden has an area of 2809 square m. How long is each side (in m)?
24. 24.What is √196? =
25. 25.What is 93²? =
26. 26.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
27. 27.How many whole numbers lie between 44² and 45²?
28. 28.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
29. 29.What is 70²? =
30. 30.What is 52²? =
31. 31.A square garden has an area of 289 square m. How long is each side (in m)?
32. 32.How many whole numbers lie between 41² and 42²?
33. 33.What is 42²? =
34. 34.How many whole numbers lie between 33² and 34²?
35. 35.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
36. 36.Which of these is a perfect square? (a) 262 (b) 256 (c) 283
37. 37.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
38. 38.Which of these is a perfect square? (a) 1501 (b) 1444 (c) 1446
39. 39.A square garden has an area of 64 square m. How long is each side (in m)?
40. 40.What is 32²? =

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