Let's analyze the given list of numbers: 2, 8, 11, 15, 21, 26, 36, 49.
### (a) Find the square numbers in the list
A square number (or perfect square) is an integer that is the square of another integer. We need to check each number in the list to see if it is a perfect square.
Upon examination of the numbers:
- 2 is not a square number.
- 8 is not a square number.
- 11 is not a square number.
- 15 is not a square number.
- 21 is not a square number.
- 26 is not a square number.
- 36 is a square number because [tex]\(6^2 = 36\)[/tex].
- 49 is a square number because [tex]\(7^2 = 49\)[/tex].
So, the square numbers in the list are 36 and 49.
### (b) Find the cube numbers in the list
A cube number (or perfect cube) is an integer that is the cube of another integer. We need to check each number in the list to see if it is a perfect cube.
Upon examination of the numbers:
- 2 is not a cube number.
- 8 is a cube number because [tex]\(2^3 = 8\)[/tex].
- 11 is not a cube number.
- 15 is not a cube number.
- 21 is not a cube number.
- 26 is not a cube number.
- 36 is not a cube number.
- 49 is not a cube number.
So the cube number in the list is 8.
### (c) Find the number with a square root of 7
We are looking for a number [tex]\(x\)[/tex] such that [tex]\( \sqrt{x} = 7\)[/tex]. Squaring both sides, we get [tex]\( x = 7^2 = 49 \)[/tex].
So the number with a square root of 7 is 49.
### Summary
- (a) Numbers that are square numbers: 36 and 49
- (b) Number that is a cube number: 8
- (c) Number with a square root of 7: 49
