Practice square roots (t2a)

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 1

Roots:

brackets 

& formulas

February 10th, 2022

t2a

11:30

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√​​​​

Schedule

• Announcements                                            5 min
• Review: simplifying square roots         10 min
• Square roots in brackets                          10 min
  
• Practice + check                                           15 min
  
• Square root formulas                                 10 min
• Tiny practice quiz                                         20 min

Announcements

• Quiz square roots: 25%       TOMORROW
• Statistics Project: 75%

Anonymous poll (be honest!):
Did you do all your homework for this lesson?

Yes

No

Review question 1:
Simplify.

3√​5​​​−7√​5​​​

1. 4√​5​​​
2. −4√​5​​​
3. −4
4. Cannot be simplified

Review question 2:
Simplify.

5√​5​​​+3√​7​​​

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

Review question 3:
Simplify.

3√​2​​​⋅4√​6​​​

1. 7√​8​​​
2. 7√​12​​​
3. 12√​8​​​
4. 12√​12​​​

Review question 4:
Factorize.

√​50​​​

1. 25√​2​​​
2. 2√​25​​​
3. 5√​2​​​
4. 2√​5​​​

Review question 5:
Factorize and simplify. Write it down!

√​50​​​+√​18​​​

1. 8√​2​​​
2. 34√​2​​​
3. √​68​​​
4. Cannot be simplified

Intended Learning Outcomes

At the end of the lesson you can...

• Work out brackets with square roots in them
• Do all sorts of calculations with square roots

Single brackets

Letters

Square roots

Double brackets

Letters

Square roots

Simplify.

√​2​​​(3√​5​​​+4)

1. 6√​5​​​+4
2. 6√​5​​​+4√​2​​​
3. 3√​10​​​+4
4. 3√​10​​​+4√​2​​​

Simplify.

(√​3​​​+2)(√​3​​​−2)

1. −1
2. 1
3. √​3​​​−4
4. √​3​​​−2

Practice

~15 min, discuss 49ad afterwards

Basic route

48, 49                                            (brackets)

62, 63, 64, 66, 67                      (later: formulas)

Advanced route

49, 50, (51)                                   (brackets)

63, 64, 65, 66, 68                      (later: formulas)

What is the graph of a quadratic formula called again?

1. Linear graph
2. Hyperbola
3. Parabola
4. Curving graph

You know two things:
- The shape of the graph of a quadratic formula
- A square root is the 'opposite' of a square
With that in mind, describe what you think the
graph of the formula on the right would look like.

y=√​x​​​

Let's build the graph

y=√​x​​​

www.geogebra.org/graphing

What will the graph of thís formula look like then?

y=−√​x​​​

1. A normal parabola again
2. A line
3. The same half sideways parabola, but going left instead of right
4. The same half sideways parabola, but going down instead of up

Explain why the following statement is/isn't true:

is the same as

y=3√​16x​​​

y=48√​x​​​

True or not true?

is the same as

y=4+√​9x​​​

y=4+3√​x​​​

1. True
2. Not true

True or not true?

is the same as

y=4+3√​x​​​

y=7√​x​​​

1. True
2. Not true

Practice...

...or practice quiz?

Basic route

48, 49                                            (brackets)

62, 63, 64, 66, 67                      (formulas)

Advanced route

49, 50, (51)                                   (brackets)

63, 64, 65, 66, 68                      (formulas)

Tiny practice quiz

• Copy the exercises in your
    notebook and solve them
• Discuss afterwards
• Done early? Continue with:

a.(5√​2​​​)−2(√​5​​​)​2​​

b.4√​3​​​+6√​7​​​−5√​3​​​

c.−2√​2​​​⋅7√​3​​​+9√​6​​​

d.2√​75​​​+4√​27​​​

e.(√​7​​​+√​8​​​)​2​​