1. find the area of a square with each side length.
a) 7 units b) 11 units
2. show that 16 is a square number. use a diagram, symbols, and words.
3. which of these numbers is a perfect square? how do you know?
a) 14 b) 60 c) 36
4. these numbers are not square numbers.
which two consecutive square numbers is each number between?
a) 7 b) 30 c) 50 d) 90

Question

1. find the area of a square with each side length.
   a) 7 units  b) 11 units
2. show that 16 is a square number. use a diagram, symbols, and words.
3. which of these numbers is a perfect square? how do you know?
   a) 14  b) 60  c) 36
4. these numbers are not square numbers.
   which two consecutive square numbers is each number between?
   a) 7  b) 30  c) 50  d) 90

Accepted Answer

### Question 1
#### Part a)
# Explanation:
## Step1: Recall the formula for the area of a square.
The area $ A $ of a square with side length $ s $ is given by $ A = s^2 $.
## Step2: Substitute the side length.
Here, $ s = 7 $ units. So, $ A = 7^2 $.
## Step3: Calculate the square.
$ 7^2 = 7\times7 = 49 $.
# Answer:
The area of the square is 49 square units.

#### Part b)
# Explanation:
## Step1: Recall the formula for the area of a square.
The area $ A $ of a square with side length $ s $ is given by $ A = s^2 $.
## Step2: Substitute the side length.
Here, $ s = 11 $ units. So, $ A = 11^2 $.
## Step3: Calculate the square.
$ 11^2 = 11\times11 = 121 $.
# Answer:
The area of the square is 121 square units.

### Question 2
# Explanation:
- **Diagram**: We can draw a square with 4 rows and 4 columns of small squares (like a 4x4 grid). Each small square has a side length of 1 unit.
- **Symbols**: A square number is a number that can be written as $ n^2 $, where $ n $ is an integer. For 16, we have $ 4^2 = 16 $ (since $ 4\times4 = 16 $).
- **Words**: A square number represents the area of a square. If we have a square with side length 4 units, the area is calculated by multiplying the side length by itself ($ 4\times4 $), which gives 16. So, 16 is the area of a square with side length 4, meaning it is a square number.
# Answer:
16 is a square number because it can be expressed as $ 4^2 $ (or $ 4\times4 $), representing the area of a 4 - unit - side - length square (shown by a 4x4 grid of unit squares).

### Question 3
# Explanation:
A perfect square (or square number) is a number that is the square of an integer, i.e., it can be written as $ n^2 $ where $ n\in\mathbb{Z} $.
- For 14: We check if there is an integer $ n $ such that $ n^2 = 14 $. The square of 3 is $ 3^2=9 $ and the square of 4 is $ 4^2 = 16 $. Since 14 is between 9 and 16 and not equal to the square of any integer, 14 is not a perfect square.
- For 60: The square of 7 is $ 7^2 = 49 $ and the square of 8 is $ 8^2=64 $. 60 is between 49 and 64 and not equal to the square of any integer, so 60 is not a perfect square.
- For 36: We know that $ 6^2=6\times6 = 36 $, so 36 is the square of the integer 6.
# Answer:
c) 36 is a perfect square. We know this because $ 6^2 = 36 $, meaning 36 is the square of the integer 6. 14 is between $ 3^2 = 9 $ and $ 4^2=16 $, and 60 is between $ 7^2 = 49 $ and $ 8^2 = 64 $, so they are not perfect squares.

### Question 4
#### Part a)
# Explanation:
We need to find two consecutive integers $ n $ and $ n + 1 $ such that $ n^2<7<(n + 1)^2 $.
- Calculate the squares of consecutive integers: $ 2^2=4 $ and $ 3^2 = 9 $.
- Since $ 4<7<9 $, we can see that 7 is between $ 2^2 $ and $ 3^2 $.
# Answer:
7 is between $ 2^2 = 4 $ and $ 3^2=9 $.

#### Part b)
# Explanation:
We need to find two consecutive integers $ n $ and $ n + 1 $ such that $ n^2<30<(n + 1)^2 $.
- Calculate the squares of consecutive integers: $ 5^2 = 25 $ and $ 6^2=36 $.
- Since $ 25<30<36 $, we can see that 30 is between $ 5^2 $ and $ 6^2 $.
# Answer:
30 is between $ 5^2 = 25 $ and $ 6^2 = 36 $.

#### Part c)
# Explanation:
We need to find two consecutive integers $ n $ and $ n + 1 $ such that $ n^2<50<(n + 1)^2 $.
- Calculate the squares of consecutive integers: $ 7^2=49 $ and $ 8^2 = 64 $.
- Since $ 49<50<64 $, we can see that 50 is between $ 7^2 $ and $ 8^2 $.
# Answer:
50 is between $ 7^2 = 49 $ and $ 8^2=64 $.

#### Part d)
# Explanation:
We need to find two consecutive integers $ n $ and $ n + 1 $ such that $ n^2<90<(n + 1)^2 $.
- Calculate the squares of consecutive integers: $ 9^2 = 81 $ and $ 10^2=100 $.
- Since $ 81<90<100 $, we can see that 90 is between $ 9^2 $ and $ 10^2 $.
# Answer:
90 is between $ 9^2 = 81 $ and $ 10^2 = 100 $.

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QUESTION IMAGE

Question

Explanation:

Question 1

Part a)

Step1: Recall the formula for the area of a square.

Step2: Substitute the side length.

Step3: Calculate the square.

Step1: Recall the formula for the area of a square.

Step2: Substitute the side length.

Step3: Calculate the square.

Answer:

Part b)