Item 24 How many blocks do you need to add to Square 6 to get Square 7? To Square 9 to get Square 10? To Square 19 to get Square 20? Explain using powers.

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