Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 703 · 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 53²? =
2. 2.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
3. 3.What is the smallest whole number by which 117 must be divided to get a perfect square?
4. 4.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
5. 5.What is 18²? =
6. 6.What is the smallest whole number by which 40 must be divided to get a perfect square?
7. 7.What is 67²? =
8. 8.What is 46²? =
9. 9.What is the smallest whole number by which 539 must be divided to get a perfect square?
10. 10.What is 45²? =
11. 11.Which of these is a perfect square? (a) 1369 (b) 1403 (c) 1436
12. 12.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
13. 13.A square garden has an area of 144 square m. How long is each side (in m)?
14. 14.Which of these is a perfect square? (a) 225 (b) 249 (c) 243
15. 15.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
16. 16.What is 30²? =
17. 17.What is 89²? =
18. 18.What is √9216? =
19. 19.What is 14²? =
20. 20.Which of these is a perfect square? (a) 148 (b) 164 (c) 144
21. 21.Which of these is a perfect square? (a) 961 (b) 1019 (c) 1014
22. 22.What is √121? =
23. 23.What is the smallest whole number by which 112 must be divided to get a perfect square?
24. 24.A square garden has an area of 1849 square m. How long is each side (in m)?
25. 25.Which of these is a perfect square? (a) 175 (b) 185 (c) 169
26. 26.What is √2025? =
27. 27.What is √1225? =
28. 28.How many whole numbers lie between 30² and 31²?
29. 29.What is 68²? =
30. 30.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
31. 31.What is √4356? =
32. 32.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
33. 33.How many whole numbers lie between 44² and 45²?
34. 34.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
35. 35.What is the smallest whole number by which 147 must be divided to get a perfect square?
36. 36.What is √4900? =
37. 37.What is 13²? =
38. 38.How many whole numbers lie between 18² and 19²?
39. 39.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
40. 40.Which of these is a perfect square? (a) 587 (b) 588 (c) 576

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