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)

...

double the previous square number and then subtract half of the previous from that.

c) is 72 a square number? explain how you determined your answer

a. no, because it is an even number
b. yes, because you can make a square shape with 72 dots
c. yes, because it is 9 squared.
d. no, because it falls between two square numbers, 8 squared and 9 squared, and there is no natural number between 8 and 9.

Explanation:

Step1: Calculate 8 squared

$8^2 = 8 \times 8 = 64$

Step2: Calculate 9 squared

$9^2 = 9 \times 9 = 81$

Step3: Compare 72 to these values

We see $64 < 72 < 81$, and there are no natural numbers between 8 and 9, so no natural number squared equals 72.

Answer:

D. No, because it falls between two square numbers, 8 squared and 9 squared, and there is no natural number between 8 and 9.