Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 8 · 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 sum of the first 20 odd numbers (1 + 3 + 5 + …)?
2. 2.Which of these is a perfect square? (a) 150 (b) 144 (c) 145
3. 3.A square garden has an area of 25 square m. How long is each side (in m)?
4. 4.What is √1369? =
5. 5.A square garden has an area of 3481 square m. How long is each side (in m)?
6. 6.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
7. 7.How many whole numbers lie between 24² and 25²?
8. 8.What is 84²? =
9. 9.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
10. 10.Which of these is a perfect square? (a) 961 (b) 973 (c) 1018
11. 11.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
12. 12.What is 79²? =
13. 13.A square garden has an area of 36 square m. How long is each side (in m)?
14. 14.What is the smallest whole number by which 27 must be divided to get a perfect square?
15. 15.What is √1296? =
16. 16.What is 85²? =
17. 17.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
18. 18.What is √676? =
19. 19.What is √3364? =
20. 20.How many whole numbers lie between 43² and 44²?
21. 21.What is the smallest whole number by which 375 must be divided to get a perfect square?
22. 22.Which of these is a perfect square? (a) 200 (b) 215 (c) 196
23. 23.How many whole numbers lie between 33² and 34²?
24. 24.What is 18²? =
25. 25.Which of these is a perfect square? (a) 107 (b) 100 (c) 104
26. 26.What is √225? =
27. 27.What is √729? =
28. 28.What is the smallest whole number by which 112 must be divided to get a perfect square?
29. 29.What is the smallest whole number by which 891 must be divided to get a perfect square?
30. 30.Which of these is a perfect square? (a) 853 (b) 867 (c) 841
31. 31.Which of these is a perfect square? (a) 1212 (b) 1165 (c) 1156
32. 32.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
33. 33.What is √7744? =
34. 34.What is √3969? =
35. 35.A square garden has an area of 1936 square m. How long is each side (in m)?
36. 36.A square garden has an area of 49 square m. How long is each side (in m)?
37. 37.How many whole numbers lie between 31² and 32²?
38. 38.A square garden has an area of 2304 square m. How long is each side (in m)?
39. 39.What is 52²? =
40. 40.What is √3025? =

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