Squareroo Math Problem

Question

If a natural number is entered into a new toy named Squareroo, the toy will do the following:

1) Find the perfect square closest to the number entered.

2) Take the square root of the perfect square

3) Find the perfect square closest to the square root found in step 2

4) Repeat the steps of taking the square root and finding closest perfect square until it takes the square root of the same number twice.

How many times does Squareroo take the square root if the number entered into it is 660?

Answer 1

Enter natural number 660.

1) Find the perfect square closest to the number entered.

Perfect squares near 660 are 625 (25²) and 676(26²). 676 is closest to 660.

2) Take the square root of the perfect square.

√676 = 26

3)

(1) Find the perfect square closest to the square root found in step 2.

Perfect squares close to 26 are 25 and 36. 25 is closest to 26.

4) Repeat the steps of taking the square root and finding closest perfect square until it takes the square root of the same number twice.

[2] √25 = 5

]3] Perfect squares close to 5 are 4 and 9.

[1] 4 is closest to 5.

[2] √4 = 2

[3] Perfect squares close to 2 are 1 and 4.

[1] 1 is closest to 2

[2] √1 = 1

[3] Perfect squares close to 1 are 1 and 1

[1] 1 is closest to 1

[2] √1 = 1

Loop ends because "until it takes the square root of the same number twice"

Count the number of times Squaroo take the square root: (2), [2], [2]. [2], [2].

5 times

Answer 2

Do not understand the process process, yet here is a start (I think):

660 = 625 + 35

660 = 25² + 25 + 10

660 = 25² + 5² + 9 + 1

660 = 25² + 5² + 3² + 1²