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Square & Cube Roots
ccss:
Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes.
Presentation Overview
Learning Objectives:
In this presentation, you will learn about:
Consider This...
Take a look at the table to the right. Can you fill in the blanks?
Use what you have already learned about exponents to help you.
n | n2 |
0 | |
| 1 |
2 | |
| 9 |
4 | |
Consider This...
Take a look at the table to the right. Can you fill in the blanks?
Use what you have already learned about exponents to help you.
n | n2 |
0 | 0 |
1 | 1 |
2 | 4 |
3 | 9 |
4 | 16 |
Review: Exponents & Squares
Remember that an exponent tells you how many times a number is repeatedly multiplied by itself.
A square is a number that is raised to the second power.
32 = 9
1.52 = 2.25
Perfect Squares
A perfect square is simply the square of a whole number.
All the numbers below are examples of perfect squares.
4 9 16 25
Can you think of another perfect square?
Square Roots
Just like multiplication and division are inverse operations, squaring a number also has an inverse operation, called a square root.
A square root of a number is a number that when multiplied by itself is equal to the given number.
We use a radical sign to indicate a square root. It looks like this:
Finding Square Roots
To find a square root, you must find the number that when multiplied by itself gives you the given number.
For example, what is the square root of 81?
81 = ?
? · ? = 81
Finding Square Roots
To find a square root, you must find the number that when multiplied by itself gives you the given number.
For example, what is the square root of 81?
81 = 9
9 · 9 = 81
You Try It!
Complete these problems on the left-side page of your interactive notebook.
1)
2)
�3)
36
144
1 16
More About Square Roots
Let's think about this problem again:
What is the square root of 81?
Is 9 the only number that when multiplied by itself will give you a product of 81?
What about -9?
81 = ?
More About Square Roots
This means that you need to find the negative square root of 81.
This means that you need to find both the positive and negative square roots of 81.
- 81
± 81
Calculating Square Roots
Use the Web 2.0 calculator to find the square root of 12.25.
3) Press the = Key
You Try It!
Complete these problems on the left-side page of your interactive notebook.
4)
5)
�6)
15
32
- 0.75
Estimating Square Roots
You can use what you know about perfect squares to estimate square roots.
√38 ≈ ?
STEP 1 - Find the perfect square the number is closest to.
36 < 38 < 49
38 is closest to 36
�STEP 2 - Use the square root of the closest perfect square as the whole number estimate.
√36 = 6
Estimating Square Roots
You can use what you know about perfect squares to estimate square roots.
√38 ≈ 6
STEP 1 - Find the perfect square the number is closest to.
36 < 38 < 49
38 is closest to 36
�STEP 2 - Use the square root of the closest perfect square as the whole number estimate.
√36 = 6
You Try It!
Complete these problems on the left-side page of your interactive notebook.
7)
8)
�9)
3
88
- 120
Cube Roots
Just like squaring a number also has an inverse operation called a square root, cubing a number has an inverse operation called a cube root.
A cube root is a number that when multiplied three times equals a given number.
The symbol for cube roots looks like this:
Cube Roots
For example, the cube root of 27 is 3.
This is because 3 · 3 · 3 = 27
What is the cube root of 64?
27 = 3
Calculating Cube Roots
Try to think of a number that when cubed equals 343.
1) Test some numbers (you can use a calculator)
2) Try making a list of cubes
You Try It!
Complete these problems on the left-side page of your interactive notebook.
10)
11) ∛1728
�12) ∛512
∛125
Pop Quiz!
Classwork:
Try these interactive games for Roots, Squares and Cubes:
**Prodigi: Squares and Cube Roots**
HW: Finding Squares and Square Roots (may use a calculator)