3Tvwo §9.2 Calculating with square roots

§9.2 Calculating with square roots

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§9.2 Calculating with square roots

Off we go!

Slide 1 - Diapositive

Square roots ... You've met these ruddy fellas many times before.

In this lesson old and new are mingled ...

Slide 2 - Diapositive

A. Watch the following examples.

_______ = =

(cbs is short for 'cannot be shortened'-funny isn't it?)

6 \sqrt ​ 5 ​ ​ ​ + 3 \sqrt ​ 5 ​ ​ ​ = 9 \sqrt ​ 5 ​ ​ ​

\sqrt ​ 8 ​ ​ ​ + \sqrt ​ 7 ​ ​ ​ = c b s

\sqrt ​ 3 ​ ​ ​

\sqrt ​ 36 ​ ​ ​

\sqrt ​ 12 ​ ​ ​

\sqrt ​ \frac{​ 3 6 ​ ​}{​ 1 2 ​} ​ ​ ​

Slide 3 - Diapositive

The rules for x and : with roots.

Some questions come up, now.

Slide 4 - Diapositive

B. Simplifying roots (2nd form stuff),

but that's been a long time ...

So you rewrite a root as:

a multiplication of 2 roots, so that

one of them comes out! In the examples:

!! Take the greatest 'outcoming' root there is !!

\sqrt ​ 12 ​ ​ ​ = \sqrt ​ 4 ​ ​ ​ \sqrt ​ 3 ​ ​ ​

\sqrt ​ 72 ​ ​ ​ = \sqrt ​ 36 ​ ​ ​ \sqrt ​ 2 ​ ​ ​ = 6 \sqrt ​ 2 ​ ​ ​

\sqrt ​ 36 ​ ​ ​ = 6

\sqrt ​ 4 ​ ​ ​ = 2

2 \sqrt ​ 3 ​ ​ ​

= 2 \sqrt ​ 3 ​ ​ ​

\sqrt ​ 72 ​ ​ ​ = \sqrt ​ 36 ​ ​ ​

\sqrt ​ 2 ​ ​ ​

\sqrt ​ 2 ​ ​ ​ = 6 \sqrt ​ 2 ​ ​ ​

\sqrt ​ 12 ​ ​ ​ = \sqrt ​ 4 ​ ​ ​

\sqrt ​ 3 ​ ​ ​

Slide 5 - Diapositive

Question 1: Simplify:

Key in your choice, in next slide.

Remember what to key in! (I cannot key in roots in a M.C. question!)

A. x B.

C. D.

\sqrt ​ 27 ​ ​ ​

\sqrt ​ 9 ​ ​ ​

\sqrt ​ 3 ​ ​ ​

3 \sqrt ​ 3 ​ ​ ​

27

\sqrt ​ 27 ​ ​ ​

Slide 6 - Diapositive

Simplify

​ [?] ​ ​ \sqrt ​ 27 ​ ​ ​

root 9 x root 3

3 root 3

root 27

Slide 7 - Quiz

Solution question 1:

= 3

\sqrt ​ 27 ​ ​ ​ = \sqrt ​ 9 ​ ​ ​

\sqrt ​ 3 ​ ​ ​

\sqrt ​ 3 ​ ​ ​

Slide 8 - Diapositive

Just like in Class,

if you have at least a 7.5 ON AVERAGE for MATH,

you may choose to leave now and work out §9.2 for yourself!

The reasons I did not offer you this possibility are:

+ in the present situation it brings us a bit closer doing sth. together

+ we only have one meet per week, most of the time

+ to be honest I like it very much having you all in the Lesson,

+ because you are a fine class, made out of fine individuals

+ still I can imagine some of you prefer now to do it by themselves

+ at least watch the following subtle root joke

Slide 9 - Diapositive

Slide 10 - Diapositive

so, pupils from C3X, with marks higher than 7.5 :

Mette, Milou, Ruby, Remco, Julie, Jochem and Ferry,

if you like to,

leave the LessonUp and do §9.2 by yourself now.

Bye!

Slide 11 - Diapositive

so, pupils from G3X, with marks higher than 7.5 :

Koen, Arul, Lieve, Soraya, Ids, Ymme, Paul, Alex, Mats, Faith,

and Doris,

If you like, leave this LessonUp now and do

§9.2 by yourself.

Bye!

Slide 12 - Diapositive

Now a more difficult one ...

Simplify

in 'the best way'.

(Decide for youself what is the best way!)

Key in your answer in the next slide again.

\sqrt ​ 72 ​ ​ ​

Slide 13 - Diapositive

Question 2:
How to simplify root 72 ?

Slide 14 - Carte mentale

Solution Question 2:

= x = 6 x

So ' the best way' is with the greatest root that comes out!

Also possible is: = x = 3 x ,

but then has to be worked out further,

and finally you get the same result!

\sqrt ​ 72 ​ ​ ​

\sqrt ​ 36 ​ ​ ​

\sqrt ​ 2 ​ ​ ​

\sqrt ​ 2 ​ ​ ​

\sqrt ​ 72 ​ ​ ​

\sqrt ​ 9 ​ ​ ​

\sqrt ​ 8 ​ ​ ​

\sqrt ​ 8 ​ ​ ​

\sqrt ​ 8 ​ ​ ​

Slide 15 - Diapositive

Question 3: What is the 'new thing' in the Theory below?

I thought we already talked about x and : with roots?!

Slide 16 - Diapositive

What's new?!

Slide 17 - Carte mentale

Solution 3:

The principal new thing is that LETTERS in stead of NUMBERS are used!

But the same rules apply.

Slide 18 - Diapositive

Slide 19 - Diapositive

Question 4:

Give the best answer:

________ =

\sqrt ​ 88 ​ ​ ​

\sqrt ​ 22 ​ ​ ​

Slide 20 - Diapositive

​ [?] ​ ​ \sqrt ​ 88 ​ ​ ​

​ [?] ​ ​ \sqrt ​ 22 ​ ​ ​

____ =

Slide 21 - Carte mentale

Question 4:

Give the best answer:

________ = = = 2 (!)

\sqrt ​ 88 ​ ​ ​

\sqrt ​ 22 ​ ​ ​

\sqrt ​ 4 ​ ​ ​

\sqrt ​ \frac{​ 8 8 ​ ​}{​ 2 2 ​} ​ ​ ​

Slide 22 - Diapositive

There is a big difference in possibilities between:

times/divided by and plus/minus with ROOTS:

Slide 23 - Diapositive

Do you know Kim?

She lives in Oxford and has a cute dog.

No expert on Maths but she knows something about it.

In the next slide you see here work on Roots!

In the slide after that one, KEY IN the CORRECT answers!

Slide 24 - Diapositive

Slide 25 - Diapositive

options for question 5:

A 1 and 3 correct B 2 and 3 correct

C 5 and 7 correct D 2 and 4 correct

Slide 26 - Diapositive

Question 5:
Kim's correct answers are:

1 and 3

2 and 3

6 and 7

2 and 4

Slide 27 - Quiz

Solution 5:

1: wrong; you cannot add roots like that!

2. correct, according to the rule for multiplication of roots

3. wrong, or did you think that + = ?!

in that case: 4 + 3 = 5 ??!

4. correct, because they are the terms we like: like terms!

\sqrt ​ 16 ​ ​ ​

\sqrt ​ 9 ​ ​ ​

\sqrt ​ 25 ​ ​ ​

Slide 28 - Diapositive

Homework time

Do §9.2 now,

skipping: 17a and b, but doing 17c!

By the way, I will again comment on some of your homeworkslides.

Bye for now!

Slide 29 - Diapositive