Practice square roots (t2a)

Roots:

brackets

& formulas

February 3rd, 2023

t2a

13:15

Log into the LessonUp with the code below!

\sqrt ​ ​ ​ ​

1 / 36

Slide 1: Slide

WiskundeMiddelbare schoolvwoLeerjaar 1

This lesson contains 36 slides, with interactive quizzes and text slides.

Lesson duration is: 60 min

Items in this lesson

Roots:

brackets

& formulas

February 3rd, 2023

t2a

13:15

Log into the LessonUp with the code below!

\sqrt ​ ​ ​ ​

Slide 1 - Slide

Schedule

Announcements 5 min
Starting up
Review: Gooseboard 20 min
Square roots in brackets 10 min
Practice 15 min
Square root formulas 10 min
Tiny practice quiz 15 min

Slide 2 - Slide

Announcements

Quiz square roots: 25% MONDAY
Statistics Project: 75% (term 4)

Slide 3 - Slide

Announcements

Got It:
60% (Thursday before test week)

Slide 4 - Slide

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

Yes

Slide 5 - Poll

1. Simplify.

3 \sqrt ​ 5 ​ ​ ​ - 7 \sqrt ​ 5 ​ ​ ​

Slide 6 - Slide

2. Simplify.

5 \sqrt ​ 5 ​ ​ ​ + 3 \sqrt ​ 7 ​ ​ ​

Slide 7 - Slide

3. Simplify.

3 \sqrt ​ 2 ​ ​ ​ \cdot 4 \sqrt ​ 6 ​ ​ ​

Slide 8 - Slide

4. Simplify.

\sqrt ​ 50 ​ ​ ​

Slide 9 - Slide

5. Simplify.

\sqrt ​ 18 ​ ​ ​

Slide 10 - Slide

6. Factorize both square roots, then simplify and add them together:

\sqrt ​ 50 ​ ​ ​ + \sqrt ​ 18 ​ ​ ​

Slide 11 - Slide

Review question 1:
Simplify.

3 \sqrt ​ 5 ​ ​ ​ - 7 \sqrt ​ 5 ​ ​ ​

4 \sqrt ​ 5 ​ ​ ​

- 4 \sqrt ​ 5 ​ ​ ​

- 4

Cannot be simplified

Slide 12 - Quiz

Review question 2:
Simplify.

5 \sqrt ​ 5 ​ ​ ​ + 3 \sqrt ​ 7 ​ ​ ​

8 \sqrt ​ 12 ​ ​ ​

8 \sqrt ​ 35 ​ ​ ​

15 \sqrt ​ 12 ​ ​ ​

Cannot be simplified

Slide 13 - Quiz

Review question 3:
Simplify.

3 \sqrt ​ 2 ​ ​ ​ \cdot 4 \sqrt ​ 6 ​ ​ ​

7 \sqrt ​ 8 ​ ​ ​

7 \sqrt ​ 12 ​ ​ ​

12 \sqrt ​ 8 ​ ​ ​

12 \sqrt ​ 12 ​ ​ ​

Slide 14 - Quiz

Review question 4:
Factorize.

\sqrt ​ 50 ​ ​ ​

25 \sqrt ​ 2 ​ ​ ​

2 \sqrt ​ 25 ​ ​ ​

5 \sqrt ​ 2 ​ ​ ​

2 \sqrt ​ 5 ​ ​ ​

Slide 15 - Quiz

Review question 4:
Factorize.

\sqrt ​ 18 ​ ​ ​

9 \sqrt ​ 2 ​ ​ ​

2 \sqrt ​ 9 ​ ​ ​

2 \sqrt ​ 3 ​ ​ ​

3 \sqrt ​ 2 ​ ​ ​

Slide 16 - Quiz

Review question 5:
Factorize, then simplify. Write it down!

\sqrt ​ 50 ​ ​ ​ + \sqrt ​ 18 ​ ​ ​

8 \sqrt ​ 2 ​ ​ ​

34 \sqrt ​ 2 ​ ​ ​

\sqrt ​ 68 ​ ​ ​

Cannot be simplified

Slide 17 - Quiz

Intended Learning Outcomes

At the end of the lesson you can...

Work out brackets with square roots in them
Draw the graph of a square root formula:
Do calculations with square root formulas

y = \sqrt ​ x ​ ​ ​

Slide 18 - Slide

Intended Learning Outcomes

At the end of the lesson you can...

Work out brackets with square roots in them
Draw the graph of a square root formula:
Do calculations with square root formulas

y = \sqrt ​ x ​ ​ ​

Take notes!

Slide 19 - Slide

Single brackets Double brackets

Letters

Square roots

Letters

Square roots

Slide 20 - Slide

Simplify.

\sqrt ​ 2 ​ ​ ​ (3 \sqrt ​ 5 ​ ​ ​ + 4)

6 \sqrt ​ 5 ​ ​ ​ + 4

6 \sqrt ​ 5 ​ ​ ​ + 4 \sqrt ​ 2 ​ ​ ​

3 \sqrt ​ 10 ​ ​ ​ + 4

3 \sqrt ​ 10 ​ ​ ​ + 4 \sqrt ​ 2 ​ ​ ​

Slide 21 - Quiz

Simplify.

(\sqrt ​ 3 ​ ​ ​ + 2) (\sqrt ​ 3 ​ ​ ​ - 2)

- 1

1

\sqrt ​ 3 ​ ​ ​ - 4

\sqrt ​ 3 ​ ​ ​ - 2

Slide 22 - Quiz

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)

Slide 23 - Slide

Slide 24 - Slide

What is the graph of a quadratic formula called again?

Linear graph

Hyperbola

Parabola

Curving graph

Slide 25 - Quiz

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 = \sqrt ​ x ​ ​ ​

Slide 26 - Open question

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, think about what the

graph of the formula above would look like.

y = \sqrt ​ x ​ ​ ​

Slide 27 - Slide

Let's build the graph

y = \sqrt ​ x ​ ​ ​

Slide 28 - Slide

www.geogebra.org/graphing

Slide 29 - Slide

What will the graph of thís formula look like then?

y = - \sqrt ​ x ​ ​ ​

A normal parabola again

A line

The same half sideways parabola, but going left instead of right

The same half sideways parabola, but going down instead of up

Slide 30 - Quiz

Think about...

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

is the same as

y = 3 \sqrt ​ 16 x ​ ​ ​

y = 48 \sqrt ​ x ​ ​ ​

Slide 31 - Slide

True or false?

is the same as

y = 4 + \sqrt ​ 9 x ​ ​ ​

y = 4 + 3 \sqrt ​ x ​ ​ ​

True

False

Slide 32 - Quiz

True or false?

is the same as

y = 4 + 3 \sqrt ​ x ​ ​ ​

y = 7 \sqrt ​ x ​ ​ ​

True

False

Slide 33 - Quiz

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)

Slide 34 - Slide

Slide 35 - Slide

Tiny practice quiz

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

(5 \sqrt ​ 2 ​ ​ ​)^{​ 2 ​ ​} - 2 (\sqrt ​ 5 ​ ​ ​)^{​ 2 ​ ​}

4 \sqrt ​ 3 ​ ​ ​ + 6 \sqrt ​ 7 ​ ​ ​ - 5 \sqrt ​ 3 ​ ​ ​

- 2 \sqrt ​ 2 ​ ​ ​ \cdot 7 \sqrt ​ 3 ​ ​ ​ + 9 \sqrt ​ 6 ​ ​ ​

2 \sqrt ​ 75 ​ ​ ​ + 4 \sqrt ​ 27 ​ ​ ​

(\sqrt ​ 7 ​ ​ ​ + \sqrt ​ 8 ​ ​ ​)^{​ 2 ​ ​}

Slide 36 - Slide

Practice square roots (t2a)

Items in this lesson

Slide 1 - Slide

Slide 2 - Slide

Slide 3 - Slide

Slide 4 - Slide

Slide 5 - Poll

Slide 6 - Slide

Slide 7 - Slide

Slide 8 - Slide

Slide 9 - Slide

Slide 10 - Slide

Slide 11 - Slide

Slide 12 - Quiz

Slide 13 - Quiz

Slide 14 - Quiz

Slide 15 - Quiz

Slide 16 - Quiz

Slide 17 - Quiz

Slide 18 - Slide

Slide 19 - Slide

Slide 20 - Slide

Slide 21 - Quiz

Slide 22 - Quiz

Slide 23 - Slide

Slide 24 - Slide

Slide 25 - Quiz

Slide 26 - Open question

Slide 27 - Slide

Slide 28 - Slide

Slide 29 - Slide

Slide 30 - Quiz

Slide 31 - Slide

Slide 32 - Quiz

Slide 33 - Quiz

Slide 34 - Slide

Slide 35 - Slide

Slide 36 - Slide

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