Answer:
You need to add 13 blocks to square 6 to get square 7
You need to add 19 blocks to square 9 to get square 10
You need to add 39 blocks to square 19 to get square 20
Step-by-step explanation:
* Lets explain how to solve the problem
- If we have two consecutive numbers n and (n + 1)
- Their squares are n² and (n + 1)²
- Lets find their difference
∵ Their difference = (n + 1)² - n²
- Solve the bracket (n + 1)²
∵ (n + 1)² = (n)(n) + 2(n)(1) + (1)(1)
∴ (n + 1)² = n² + 2n + 1
∴ Their difference = n² + 2n + 1 - n²
- Add the like terms
∴ Their difference = 2n + 1
- Lets use this rule to find the number of blocks we need to add to:
# square 6 to get square 7
∵ 6 and 7 are two consecutive numbers
∴ n = 6
∴ Their difference = 2(6) + 1 = 12 + 1 = 13
∴ You need to add 13 blocks to square 6 to get square 7
# square 9 to get square 10
∵ 9 and 10 are two consecutive numbers
∴ n = 9
∴ Their difference = 2(9) + 1 = 18 + 1 = 19
∴ You need to add 19 blocks to square 9 to get square 10
# square 19 to get square 20
∵ 19 and 20 are two consecutive numbers
∴ n = 19
∴ Their difference = 2(19) + 1 = 38 + 1 = 39
∴ You need to add 39 blocks to square 19 to get square 20
