Simplifying square roots (t2a)

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 1

Simplifying square roots

January 30th, 2023

t2a

8:30

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Schedule

• Starting up                                                        5 min
• Review: square roots                                  15 min
    + hw-check
• Simplifying square roots                          15 min
  
• (Silent) practice                                            20 min
  
• Gooseboard!                                                  20 min

Announcements

Don't forget GOT IT!

Deadline: Thursday before test week

Review (+hw-check)

1. A square field has an area of 400 m². The sides get painted white for a tournament. The paint costs 3.50 per meter.
   How much does it cost to paint all four sides?
2. Solve: 
3. Solve: 
4. Solve: 

2(√​400​​​−√​49​​​)

(√​9​​​)​2​​

(3√​7​​​)​2​​

Review question 1:
A square field of grass has an area of

What is the perimeter?

400

m​2​​

1. 400 m
2. 100 m
3. 80 m
4. 40 m

Review question 2:
A square field of grass has an area of

What is the length of one of the sides?

50

m​2​​

1. 7.07 m
2. 12.5 m
3. 25 m
4. It's impossible to tell

Review question 3:
Solve.

2(√​400​​​−√​49​​​)

1. 1.8
2. 26
3. 33
4. 698

Review question 4:
Solve.

(√​9​​​)​2​​

1. 3
2. 9
3. 81
4. Cannot be simplified

Review question 5:
Simplify.

(3√​7​​​)​2​​

1. 21
2. 23.8
3. 63
4. 147

Intended Learning Outcomes

At the end of the lesson you can...

• Calculate squares of square roots
• Multiply and add square roots
• Simplify square roots by factorizing

Intended Learning Outcomes

At the end of the lesson you can...

• Calculate squares of square roots
• Multiply and add square roots
• Simplify square roots by factorizing

Make notes!!!

Squares of square roots

(3√​7​​​)​2​​

(5√​2​​​)​2​​

7(√​8​​​)​2​​

Adding square roots

Letters

Square roots

Adding square roots

Rule for adding square roots:

Just as with letters, only add like roots, otherwise not possible!

Letters

Square roots

Simplify.

5√​5​​​+3√​7​​​

1. 8√​12​​​
2. 8√​35​​​
3. 15√​12​​​
4. Cannot be simplified

Simplify.

5√​7​​​−9√​7​​​

1. 4√​7​​​
2. -28
3. −4√​7​​​
4. Cannot be simplified

Multiplying square roots

5√​2​​​⋅√​7​​​

3√​5​​​⋅4√​10​​​

8√​2​​​⋅2√​8​​​

Simplify.

3√​3​​​⋅2√​24​​​

1. 5√​27​​​
2. 5√​72​​​
3. 6√​27​​​
4. 6√​72​​​

Factorizing square roots

3√​5​​​⋅4√​10​​​

3√​3​​​⋅2√​24​​​

Simplify and factorize. Take your time!

3√​3​​​⋅2√​24​​​

1. 36√​2​​​
2. 2√​36​​​
3. 12
4. 6√​2​​​

Practice

 

                                                                                      (squaring square roots)

                                                                                      (adding & multiplying square roots)

                                                                                      (factorizing square roots)

Advanced route

31

34, 37, 38, 39

41, 44, 45

Basic route

30def, 31abc 

35, 36, 37, 38

42, 43, 44

Check:
Simplify, then factorize. Take your time!

2√​6​​​⋅√​27​​​

1. 18
2. 9√​2​​​
3. 18√​2​​​
4. 9√​3​​​

Gooseboard!