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.
□, □, □

Explanation:

Step1: Identify square number pattern

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

Step2: Find next $n$ values

Given last number is $25=5^2$, next $n=6,7,8$.

Step3: Calculate $6^2$

$6^2 = 6\times6 = 36$

Step4: Calculate $7^2$

$7^2 = 7\times7 = 49$

Step5: Calculate $8^2$

$8^2 = 8\times8 = 64$

Answer:

36, 49, 64