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 \(\(6^2 = 36\)\).
- 49 is a square number because \(\(7^2 = 49\)\).
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 \(\(2^3 = 8\)\).
- 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 \(\(x\)\) such that \(\( \sqrt{x} = 7\)\). Squaring both sides, we get \(\( x = 7^2 = 49 \)\).
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
