1. Square and Square Roots; Cubes and Cube Roots

2. First Name Last Name Date Period Assignment
Must ALWAYS have this heading!!
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:

3. 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.

4. 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

5. 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

6. 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)

7. What are the perfect squares of 1-15?
Study questions:
What are the perfect squares of 1-15?
What are the perfect cubes of 1-5?

8. 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.

9. 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?

10. 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=
√25=
3√64=
What number is a perfect square and a perfect cube? Show how you know.

11. 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
√25=5
3√64=4
What number is a perfect square and a perfect cube? Show how you know. 64!
8x8=64 4x4x4=64

12. 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.

13. Let’s practice!
Estimate the square root of… √40 √72 √23

14. 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

15. Study question:
How do you ESTIMATE the square root of a number that is NOT a perfect square?

16. Summary
In 4-5 sentences, answer the essential question. Use some of these words:
Perfect square
Perfect cube
Square root
Cube root
estimate