Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 549 · 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 90²? =
2. 2.What is 30²? =
3. 3.What is 32²? =
4. 4.What is √1156? =
5. 5.What is 72²? =
6. 6.What is 82²? =
7. 7.What is √9216? =
8. 8.What is √441? =
9. 9.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
10. 10.A square garden has an area of 144 square m. How long is each side (in m)?
11. 11.What is the smallest whole number by which 243 must be divided to get a perfect square?
12. 12.A square garden has an area of 36 square m. How long is each side (in m)?
13. 13.What is √729? =
14. 14.How many whole numbers lie between 33² and 34²?
15. 15.How many whole numbers lie between 9² and 10²?
16. 16.A square garden has an area of 676 square m. How long is each side (in m)?
17. 17.What is 24²? =
18. 18.A square garden has an area of 2304 square m. How long is each side (in m)?
19. 19.How many whole numbers lie between 35² and 36²?
20. 20.What is 42²? =
21. 21.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
22. 22.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
23. 23.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
24. 24.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
25. 25.A square garden has an area of 1369 square m. How long is each side (in m)?
26. 26.A square garden has an area of 49 square m. How long is each side (in m)?
27. 27.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
28. 28.Which of these is a perfect square? (a) 820 (b) 810 (c) 784
29. 29.What is the smallest whole number by which 240 must be divided to get a perfect square?
30. 30.Which of these is a perfect square? (a) 918 (b) 900 (c) 953
31. 31.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
32. 32.What is √1024? =
33. 33.How many whole numbers lie between 48² and 49²?
34. 34.A square garden has an area of 1225 square m. How long is each side (in m)?
35. 35.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
36. 36.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
37. 37.How many whole numbers lie between 14² and 15²?
38. 38.Which of these is a perfect square? (a) 1327 (b) 1345 (c) 1296
39. 39.How many whole numbers lie between 44² and 45²?
40. 40.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?

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