Unit 27: Perfect Squares
In this unit, you will identify numbers and variables that are perfect squares. Then you will solve equations involving perfect squares.
Section 1- Perfect Square Numbers
A perfect square is a number that is the result of one number multiplied by itself.
Examples of perfect squares:
4
2 times itself equals 4
25
5 times itself equals 25
List of first 10 perfect squares:
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| The perfect squares are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
Another way to state these perfect squares is: |
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| Section 2 - Perfect Square Variables
Perfect squares can also be represented as variables. Sometimes a number is unknown, therefore, we use a variable to represent that number. Perfect square variables look like the following: |
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| The perfect square variables mentioned here are x2, y2, a2, and m2.
Notice that all perfect square variables are raised to the second power. Hence, the variable is squared. |
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| Section 3 - Perfect Square Equations
To solve a perfect square equation, use the reverse order of operations, PEMDAS backwards. When you get to the E of PEMDAS, meaning exponents, the opposite of squaring a number is taking the square root. You can also think of it as “what number times itself equals this number.” Note, in this case there will be two answers (except when or any negative number). The two answers will be the positive value and the negative value of that square root. See the example below.
Example 1. Solve for x. |
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| Because 6 x 6 = 36 AND -6 x -6 = 36
Answer: x = 6 or x -6 |
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| Example 2. Solve for r.
r2 + 1 = 10
1) Using PEMDAS backwards, subtract 1 from both sides of the equation.
r2 + 1 = 10
- 1 -1
r2 = 9
2) Take the square root of both sides of the equation to get rid of the exponent. |
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| Answer: r = 3 or r = -3
STOP: Click on the Unit icon and complete Practice 1. |
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| 2) 15+15=
A. 152
B. 15•15
C. 15•2 |
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| 6) * |
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| Correct! |
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| Select the letter of the number that is a perfect square. |
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| 7) Which number is a perfect square? |
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| Correct! |
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| 8) Which number is a perfect square? |
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| Correct! |
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| 9) Which number is a perfect square? (Note: This perfect square is not stated in the lesson. Find it by multiplying numbers by themselves or by taking the square root of each answer choice.) |
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| 10) 1 square yard = __ square feet
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| Correct! |
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| 11) 1 square foot = __ square inches |
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| 13) square units (square feet, square yards, square inches) are 2-dimensional units of measurement typically used to cover surface.
Which is an example of covering a surface? |
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| Correct! |
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| Read the directions carefully to determine which letter answer to select. |
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| 14) Which variable expression is a perfect square? |
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| Correct! |
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| 15) Which variable expression forms a perfect square? |
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| Correct! |
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| Select the letter of the solution to each equation. |
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| 16) Solve for m.
m2 = 25
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| Correct! |
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| 17) Solve the equation:
m2 = 196 |
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| 18) Which equation has no solutions?
A. x2 = 0
B. x2 = 1
C. x2 = -1 |
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| Incorrect |
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| 19) Which equation has only 1 solution?
A. x2 = 0
B. x2 = 1
C. x2 = -1 |
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| Incorrect |
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| 20) Solve for w.
w2 - 1 = 63 |
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| Correct! |
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| 21) Solve for a.
2a2 = 200 |
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| Correct! |
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| 22) Solve for p.
3p2 + 1 = 4 |
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| Correct! |
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| 23) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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