Question

an ancient culture labeled certain numbers as square numbers. the numbers 1, 4, 9, 16, 25, and so on are square numbers. complete parts a through c below.
(image of dot arrays representing 1, 4, 9, 16, 25)

a) determine the next three square numbers.
36, 49, 64

b) describe a procedure to determine the next five square numbers without drawing the figures.
a. square 6, 7, 8, 9, and 10
b. square 6, 8, 10, 12, and 14
c. add the last two square numbers together to get the next one
d. double the previous square number and then subtract half of the previous from that

Explanation:

Step1: Identify square number pattern

Square numbers are $n^2$ where $n$ is positive integer.

Step2: Solve part (a)

Next integers after 5: 6,7,8.
$6^2=36$, $7^2=49$, $8^2=64$

Step3: Evaluate part (b) options

Option A uses the definition $n^2$ for consecutive integers.
Options B,C,D do not follow square number rules.

Answer:

a) 36, 49, 64
b) A. Square 6, 7, 8, 9, and 10