Square and Square Roots;
Cubes and Cube Roots
First Name Last NameDate
PeriodAssignment
Essential Question: What are perfect squares and cubes, what are their square and cube roots, and how do I find the root of a non-perfect square?
Study Questions: Notes:
Must ALWAYS have this heading!!
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!
• Area: Area= 3x3 or 32 or 9
3
3
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
333
33
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)
***you will need to know all the way to 225!
• Lets list all the perfect cubes from 1-125! 1, 8, 27, 64, 125 (13, 23, 33, 43, 53)
Study questions:
What are the perfect squares of 1-15?
What are the perfect cubes of 1-5?
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:
1. What is the value of 5 cubed?
2. What is the value of 2 squared?
3. √16=
4.√25=
5.3√64=
6.What number is a perfect square and a perfect cube? Show how you know.
Practice
• Let's practice what we just learned:
1. What is the value of 5 cubed? 125
2. What is the value of 2 squared? 4
3. √16=4
4.√25=5
5.3√64=4
6.What number is a perfect square and a perfect cube? Show how you know. 64!
8x8=64 4x4x4=64
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…
√40
√72
√23
Let’s practice!Estimate the square root of…
√40
We know √36 is 6 and √49 is 7, so √40
is BETWEEN 6 and 7
√72
We know √64 is 8 and √81 is 9, so √72
is BETWEEN 8 and 9
√23 We know √16 is 4 and √25 is 5, so √23
is BETWEEN 4 and 5
Study question:
How do you ESTIMATE the square root of a number that is NOT a
perfect square?
Summary
In 4-5 sentences, answer the essential question. Use some of these words:
• Perfect square
• Perfect cube
• Square root
• Cube root
• estimate