Lesson 1
Square and Square Roots;
Cubes and Cube Roots
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.
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!
3
• Area:
3
Area= 3x3 or 32
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
3
33
3
3
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?
Any questions so far?
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.
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?
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.
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
And your homework is…