Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 596 · 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 √169? =
2. 2.What is √2025? =
3. 3.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
4. 4.Which of these is a perfect square? (a) 623 (b) 576 (c) 620
5. 5.What is 19²? =
6. 6.What is 13²? =
7. 7.A square garden has an area of 400 square m. How long is each side (in m)?
8. 8.A square garden has an area of 361 square m. How long is each side (in m)?
9. 9.Which of these is a perfect square? (a) 1398 (b) 1369 (c) 1396
10. 10.What is √625? =
11. 11.What is √3025? =
12. 12.What is 58²? =
13. 13.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
14. 14.What is 17²? =
15. 15.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
16. 16.A square garden has an area of 3249 square m. How long is each side (in m)?
17. 17.What is √1296? =
18. 18.Which of these is a perfect square? (a) 256 (b) 262 (c) 284
19. 19.Which of these is a perfect square? (a) 330 (b) 326 (c) 324
20. 20.How many whole numbers lie between 25² and 26²?
21. 21.A square garden has an area of 1681 square m. How long is each side (in m)?
22. 22.Which of these is a perfect square? (a) 100 (b) 102 (c) 105
23. 23.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
24. 24.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
25. 25.What is 78²? =
26. 26.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
27. 27.What is the smallest whole number by which 468 must be divided to get a perfect square?
28. 28.What is √7744? =
29. 29.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
30. 30.What is 39²? =
31. 31.How many whole numbers lie between 37² and 38²?
32. 32.A square garden has an area of 324 square m. How long is each side (in m)?
33. 33.Which of these is a perfect square? (a) 858 (b) 861 (c) 841
34. 34.A square garden has an area of 289 square m. How long is each side (in m)?
35. 35.What is √2704? =
36. 36.Which of these is a perfect square? (a) 739 (b) 778 (c) 729
37. 37.What is √441? =
38. 38.What is 31²? =
39. 39.How many whole numbers lie between 22² and 23²?
40. 40.What is the smallest whole number by which 252 must be divided to get a perfect square?

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