Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 522 · 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 smallest whole number by which 126 must be divided to get a perfect square?
2. 2.A square garden has an area of 529 square m. How long is each side (in m)?
3. 3.What is 64²? =
4. 4.Which of these is a perfect square? (a) 1527 (b) 1521 (c) 1543
5. 5.What is 20²? =
6. 6.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
7. 7.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
8. 8.What is 91²? =
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) 202 (b) 196 (c) 216
11. 11.What is 93²? =
12. 12.A square garden has an area of 3025 square m. How long is each side (in m)?
13. 13.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
14. 14.What is √5476? =
15. 15.What is 25²? =
16. 16.What is 31²? =
17. 17.What is 26²? =
18. 18.What is √7569? =
19. 19.Which of these is a perfect square? (a) 225 (b) 239 (c) 242
20. 20.What is √5184? =
21. 21.Which of these is a perfect square? (a) 1509 (b) 1503 (c) 1444
22. 22.How many whole numbers lie between 17² and 18²?
23. 23.What is √196? =
24. 24.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
25. 25.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
26. 26.What is √4761? =
27. 27.What is 41²? =
28. 28.What is √900? =
29. 29.A square garden has an area of 3600 square m. How long is each side (in m)?
30. 30.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
31. 31.What is √3600? =
32. 32.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
33. 33.What is √4624? =
34. 34.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
35. 35.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
36. 36.Which of these is a perfect square? (a) 102 (b) 116 (c) 100
37. 37.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
38. 38.What is √576? =
39. 39.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
40. 40.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?

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