Final answer:
The difference between the 15th and 14th square numbers is 29. To calculate this, one must square the integers 15 and 14 and subtract the latter from the former. In related examples, such as square areas, doubling the side length quadruples the area.
Step-by-step explanation:
The difference between the 15th square number and the 14th square number can be found by first identifying what these square numbers are. The nth square number is simply the product of an integer n times itself. Therefore, the 15th square number is 15×15 (which is 225) and the 14th square number is 14×14 (which is 196).
We calculate the difference by subtracting the smaller square number from the larger one: 225 - 196, which gives us the result of 29. Hence, the difference between the 15th square number and the 14th square number is 29.
In Marta's case, where she has two squares, the area of a square is calculated by the square of its side length. For the first square with a side of 4 inches, the area is 4×4 = 16 square inches. Her larger square has sides that are twice the first square, thus 8 inches. The area of the larger square is 8×8 = 64 square inches. Therefore, the larger square's area is exactly four times the smaller square's area because when the side length is doubled, the area increases by a factor of the side length squared, in this case, 2×2 = 4.