To solve these equations, we need to find the value of the variable that, when multiplied by itself, equals the number on the other side of the equal sign. This is called taking the square root.
For perfect squares (like 25, 9, 121), the answer is a whole number.
For numbers that aren’t perfect squares (like 50, 120, 575), we leave the answer as a square root symbol (√) with the number inside.
Let’s go step by step:
1. b² = 25 → What number times itself is 25? 5 × 5 = 25 → b = 5
2. k² = 9 → 3 × 3 = 9 → k = 3
3. v² = 121 → 11 × 11 = 121 → v = 11
4. t² = 50 → 50 isn’t a perfect square → t = √50
5. z² = 196 → 14 × 14 = 196 → z = 14
6. m² = 400 → 20 × 20 = 400 → m = 20
7. j² = 64 → 8 × 8 = 64 → j = 8
8. c² = 49 → 7 × 7 = 49 → c = 7
9. n² = 120 → Not a perfect square → n = √120
10. s² = 169 → 13 × 13 = 169 → s = 13
11. w² = 256 → 16 × 16 = 256 → w = 16
12. f² = 361 → 19 × 19 = 361 → f = 19
13. y² = 575 → Not a perfect square → y = √575
14. a² = 900 → 30 × 30 = 900 → a = 30
15. q² = 1,225 → 35 × 35 = 1,225 → q = 35
16. d² = 324 → 18 × 18 = 324 → d = 18
17. x² = 600 → Not a perfect square → x = √600
18. g² = 625 → 25 × 25 = 625 → g = 25
19. r² = 721 → Not a perfect square → r = √721
20. h² = 1,600 → 40 × 40 = 1,600 → h = 40
21. p² = 2,025 → 45 × 45 = 2,025 → p = 45
Double-checking a few tricky ones:
- √50: 7×7=49, 8×8=64 → not perfect → correct to leave as √50
- √120: 10×10=100, 11×11=121 → not perfect → correct
- √575: 23×23=529, 24×24=576 → very close but not perfect → correct
- √600: 24×24=576, 25×25=625 → not perfect → correct
- √721: 26×26=676, 27×27=729 → not perfect → correct
All answers are verified.
Final Answer:
1. b = 5
2. k = 3
3. v = 11
4. t = √50
5. z = 14
6. m = 20
7. j = 8
8. c = 7
9. n = √120
10. s = 13
11. w = 16
12. f = 19
13. y = √575
14. a = 30
15. q = 35
16. d = 18
17. x = √600
18. g = 25
19. r = √721
20. h = 40
21. p = 45
Parent Tip: Review the logic above to help your child master the concept of solving equations with square roots simplifying square roots worksheet 10 d.
