Simplifying square roots (t2a)

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 1

Simplifying square roots

February 4th, 2022

t2a

8:30

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Schedule

• Announcements                                            5 min
• Review: square roots                                  10 min
• Simplifying square roots                          15 min
  
• Practice                                                            30 min
  

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

.
What is the length of one of the sides?

400

m​2​​

1. 200 m
2. 100 m
3. 20 m
4. It's impossible to tell

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

Simplify and factorize. Take your time!

2√​6​​​⋅√​27​​​

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