1. Activating Prior Knowledge –
M7:LSN4
Simplifying Square Roots
Activating Prior Knowledge –
Write down prime factors of the following numbers.
Example 100 = 10 x 10 = 2 x 5 x 2 x 5 = 2 x 2 x 5 x 5
5∙5∙2
2∙2∙5
2∙2∙3
2∙2∙2∙2∙5
2∙2∙2∙3
2∙2∙2∙2∙3
Tie to LO

2. Today, we will use factors of a number to simplify a square root.
Learning Objective
Today, we will use factors of a number to simplify a square root.
CFU

3. Concept Development – Opening Exercise (5 mins.)
M7:LSN4
Module
Page 15
Simplifying Square Roots
Concept Development – Opening Exercise (5 mins.)
1.  
a. What does equal?
b. What does 4×4 equal?
c Does 16 = 4×4 ?
2.  
What does equal?
b. What does 6×6 equal?
c. Does 36 = 6×6 ?
CFU

4. Concept Development – Opening Exercise (5 mins.)
M7:LSN4
Module
Page 15
Simplifying Square Roots
Concept Development – Opening Exercise (5 mins.)
3.  
What does equal?
b. What does 11×11 equal?
c. Does = 11×11 ?
4.  
What does equal?
b. What does 9×9 equal?
c. Does 81 = 9×9 ?
CFU

5. CFU Concept Development Simplifying Square Roots 36 = 4×9 36 =2∙3
M7:LSN4
Simplifying Square Roots
Concept Development
We know from the last lesson that square roots can be simplified to a whole number when they are perfect squares. That is,
9 = 3×3 = = 3
Let’s look two different ways at a perfect square. What is 36 ?
36 =6.
Now consider the factors of 36. Specifically those that are perfect squares. We want to rewrite as a product of perfect squares. What will that be?
36 = 4×9
36 =2∙3
36 =6
36 =6
CFU

6. Concept Development – Pair Share
M7:LSN4
Simplifying Square Roots
Concept Development – Pair Share
Simplify two different ways. Explain your work to a partner.
64 = 8×8
64 = 16×4
64 =8
64 =4∙2
64 =8
CFU

7. Skill Development/Guided Practice – Ex #1
M7:LSN4
Module
Page 16
Simplifying Square Roots
Skill Development/Guided Practice – Ex #1
1. Simplify the square root as much as possible.
50 =
Is the number 50 a perfect square? Explain.
Since 50 is not a perfect square, when we need to simplify 50 , we write the factors of the number 50 looking specifically for those that are perfect squares.
What are the factors of 50?
50 = 25×2
Is the number 2 a perfect square?
50 =5∙ 2
is the simplified form
CFU

8. Skill Development/Guided Practice – Ex #2
M7:LSN4
Module
Page 16
Simplifying Square Roots
Skill Development/Guided Practice – Ex #2
2. Simplify the square root as much as possible.
28 =
Is the number 28 a perfect square? Explain.
Since 28 is not a perfect square, when we need to simplify 28 , we write the factors of the number 28 looking specifically for those that are perfect squares.
What are the factors of 28?
Which set of factors is better?
28 = 14×2 or 4×7
28 = 4×7
Is the number 7 a perfect square?
28 =2∙ 7
is the simplified form
CFU

9. Independent Practice – Ex. 7 – 10 (5 mins.)
M7:LSN4
Module
Page 16
Simplifying Square Roots
Independent Practice – Ex. 7 – 10 (5 mins.)
Simplify the square roots as much as possible.  
CFU

10. Skill Development/Guided Practice – Ex #3
M7:LSN4
Module
Page 17
Simplifying Square Roots
Skill Development/Guided Practice – Ex #3
3. Simplify the square root as much as possible.
128 =
Is the number 128 a perfect square? Explain.
Since 128 is not a perfect square, when we need to simplify , we write the factors of the number 28 looking specifically for those that are perfect squares.
What are the factors of 128?
Which set of factors is better?
128 = 64×2 or 4×32
128 = 64×2
Is the number 2 a perfect square?
128 =8∙ 2
is the simplified form
CFU

11. Skill Development/Guided Practice – Ex #4
M7:LSN4
Module
Page 17
Simplifying Square Roots
Skill Development/Guided Practice – Ex #4
4. Simplify the square root as much as possible.
288 =
Is the number 288 a perfect square? Explain.
Since 288 is not a perfect square, when we need to simplify , we write the factors of the number 288 looking specifically for those that are perfect squares.
What are the factors of 288?
Which set of factors is better?
288 = 72×4 or ×2
288 = 144×2
Is the number 2 a perfect square?
288 =12∙ 2
is the simplified form
CFU

12. Independent Practice – Ex. 11 – 14 (5 mins.)
M7:LSN4
Module
Page 17
Simplifying Square Roots
Independent Practice – Ex. 11 – 14 (5 mins.)
Simplify the square roots as much as possible.
11. Simplify Simplify 250
13. Simplify Simplify
CFU

13. CFU Simplifying Square Roots Module Page 18
M7:LSN4
Simplifying Square Roots
Module
Page 18
Lesson Summary
Square roots of non-perfect squares can be simplified by using the factors of the number. Any perfect square factors of a number can be simplified.
For example: = 36×2 = 36 × 2 = × 2 =6× 2 =6 2
CFU

14. Closure Homework – Module page 18-19 Problem Set #1-10 CFU
What did we learn today?
Why is it important to you?
3. How can square roots of non-perfect squares be simplified? Simplify 𝟐𝟎
Homework – Module page 18-19
Problem Set #1-10
Module
Pages
18-19
CFU

15. Homework – Module page 18-19 Problem Set #1-10
Pages
18-19
Simplify each of the square roots in Problems 1–5 as much as possible.
CFU

16. Homework – Module page 18-19 Problem Set #1-10
Pages
18-19
6. What is the length of the unknown side of the right triangle?
Simplify your answer.
7. What is the length of the unknown side of the right triangle?
Simplify your answer.
CFU

17. Homework – Module page 18-19 Problem Set #1-10
Pages
18-19
8. What is the length of the unknown side of the right triangle?
Simplify your answer.
9. Josue simplified as Is he correct? Explain why or why not.
10. Tiah was absent from school the day that you learned how to simplify a square root. Using , write Tiah an explanation for simplifying square roots.
CFU