Perfect Squares and Square Numbers

Show your work for each problem.

1.
Which of the following is a perfect square?
1. a)
2. b)
3. c)
4. d)
Answer:
. The other numbers cannot be written as a whole number times itself.
2.
What is ?
Answer: 25
. Remember, the exponent 2 means multiply the number by itself.
3.
What is ?
Answer: 7
because . The square root finds the number that was squared.
4.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
because . Note: would be half of 100, not the square root.
5.
What is ?
Answer: 64
. This is the area of a square with sides of length 8.
6.
A square garden has an area of square meters. What is the length of each side?
Answer: 9
1. What is the formula for the area of a square? s^2
2. We know area = . What operation finds the side from the area? square root
3. What is ? 9
7.
Which of these is NOT a perfect square?
1. a)
2. b)
3. c)
4. d)
Answer:
is not a perfect square. It falls between and . The other options are: , , .
8.
What is ?
Answer: 121
. Notice the pattern: , , .
9.
Is a perfect square? If not, between which two perfect squares does it fall?
Answer: 100 and 121
1. What is ? 100
2. What is ? 121
3. Is ? yes
4. So 120 is between which two perfect squares? 100 and 121
10.
What is ?
Answer: 12
because . This is the last perfect square to memorize: .
11.
A chess board has squares arranged in a perfect square grid. How many squares are on each side?
Answer: 8
1. If a grid is a perfect square with squares per side, what is the total? n^2
2. We know the total is . So . What operation finds ? square root
3. What is ? 8
12.
If , what is ?
1. a)
2. b)
3. c)
4. d)
Answer:
because . This follows in the sequence of perfect squares.
13.
The difference between two consecutive perfect squares is . What are the two perfect squares?
Answer: 144 and 169
1. Consecutive perfect squares differ by odd numbers. Is 25 odd? yes
2. If the difference is , what is ? 12
3. So the smaller square is ? 144
4. And the larger square is ? 169
14.
What is ?
Answer: 225
. Shortcut: Numbers ending in 5 follow a pattern: followed by . So , then gives .
15.
Which statement about perfect squares is TRUE?
1. a)The square of an odd number is always odd
2. b)All perfect squares are even
3. c)There are no perfect squares between 100 and 120
4. d)Perfect squares can be negative
Answer: The square of an odd number is always odd
Odd odd = odd, so the square of an odd number is always odd. Examples: , , .
16.
A square painting has an area of square centimeters. What is the perimeter of the painting?
Answer: 56
1. First find the side length. If area = , what is ? 14
2. The perimeter of a square is side. What is ? 56