Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 598 · 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 √121? =
2. 2.What is √900? =
3. 3.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
4. 4.A square garden has an area of 1369 square m. How long is each side (in m)?
5. 5.How many whole numbers lie between 8² and 9²?
6. 6.Which of these is a perfect square? (a) 1443 (b) 1369 (c) 1441
7. 7.What is 76²? =
8. 8.What is the smallest whole number by which 245 must be divided to get a perfect square?
9. 9.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
10. 10.What is 22²? =
11. 11.What is 86²? =
12. 12.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
13. 13.What is √9409? =
14. 14.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
15. 15.Which of these is a perfect square? (a) 133 (b) 125 (c) 121
16. 16.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
17. 17.What is √4096? =
18. 18.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
19. 19.Which of these is a perfect square? (a) 369 (b) 361 (c) 362
20. 20.A square garden has an area of 1225 square m. How long is each side (in m)?
21. 21.What is the smallest whole number by which 325 must be divided to get a perfect square?
22. 22.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
23. 23.What is √7396? =
24. 24.What is √1369? =
25. 25.Which of these is a perfect square? (a) 937 (b) 906 (c) 900
26. 26.What is 93²? =
27. 27.What is the smallest whole number by which 320 must be divided to get a perfect square?
28. 28.A square garden has an area of 1600 square m. How long is each side (in m)?
29. 29.What is 33²? =
30. 30.What is √3364? =
31. 31.What is 60²? =
32. 32.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
33. 33.Which of these is a perfect square? (a) 162 (b) 144 (c) 150
34. 34.How many whole numbers lie between 18² and 19²?
35. 35.How many whole numbers lie between 24² and 25²?
36. 36.What is √961? =
37. 37.What is √1089? =
38. 38.How many whole numbers lie between 22² and 23²?
39. 39.Which of these is a perfect square? (a) 294 (b) 320 (c) 289
40. 40.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?

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