1. Square and Square Roots; Cubes and Cube Roots
Lesson 1
Square and Square Roots;
Cubes and Cube Roots

2. Squares
The square of a number can be found by multiplying that number by itself.
Square the number 3: 3x3=9
Since the number 3 is multiplied twice, it is written 32.

3. Why call it “Squared?” We call it squaring from the shape!
A square is unique because all 4 sides are the same, so length and width are the same number.
When we find the area, we are really multiplying a number by itself!
Area: Area= 3x3 or 32 3 3

4. Cube Multiply that number by itself 3 times. Cube the number 6: 6x6x6
It would be written 63
Why cubed? Same idea as squared!
All sides of a cube are the same, so when we find the volume, we multiply the same number 3 times.
Volume: Volume= 3x3x3 or 33 3 3 3

5. Perfect squares and Perfect cubes
Lets list all the perfect squares from 1-100:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
(12,22,32, 42, 52, 62, 72, 82, 92, 102)
Lets list all the perfect cubes from 1-125!
1, 8, 27, 64, 125
(13, 23, 33, 43, 53)
What number is both a perfect square and cube?

6. Any questions so far?

7. Square root This is the inverse, or opposite, or squaring a number.
32= 9 so √9 = 3
A perfect square has a square root that is a whole number.
9 is a perfect square because its square root is a whole number, 3.
10 is not a perfect square because its square root is about 3.16, which is NOT a whole number.

8. Finding Square Root What is the √16?
Think back to those perfect squares… what number squared is 16? 4! So… √16= 4
What is the √81?
What is the √36?
What is the 3√27?

9. Practice Let's practice what we just learned:
- What is the value of 5 cubed?
- What is the value of 2 squared?
- What is the √16?
- What is the √25?
- What is the 3√64?
- What number is a perfect square and a perfect cube? Show how you know.

10. Taking it a step further
What about those numbers that are not perfect squares? √17 for example?!
Lets go back to that list of perfect squares… what perfect squares is close to 17?
So we can estimate the √17 to be between 4 and 5.
Let’s practice!
Estimate the square root of… √17, √40, √72, √23

11. And your homework is…