3Thavo §9.4 Calculating with square roots

• Wiskunde
• Middelbare school
• havo
• Leerjaar 3

§9.4 Calculating with square roots

 First a few slides to Refresh your memory.

In fact this is from 2nd Form.

But that was a long time ago ....

Repeating some basic knowledge about ROOTS takes some slides/time, that's true. But after this you will be

+ up to scratch with your roots again and

+ have an easier task doing §9.4, because we will practice a lot, too!

Above you see how the whole number '2' is changed into 

 and then multiplied by              .

The endresult is one single root!

​[?]​​√​4​​​

​[?]​​√​3​​​

√​4​​​

√​3​​​

Above you see 3 more examples, of:

TASK 1.   Now write as a single 

                square root yourself:

Key in your answer in the next slide.

If you cannot find the symbol for 'root', just write:

'root'!

4​[?]​​√​3​​​

4√​3​​​

Write as one root:

Solution 1:

The point stands

for multiplying!

4​[?]​​√​3​​​=​[?]​​√​16​​​​[?]​​√​3​​​=​[?]​​√​48​​​

4√​3​​​

4√​3​​​=√​16​​​⋅√​3​​​=√​48​​​

Task 2.   Write as one root:

Choose in the next slide between (remember your choice!):

A.                                 B. 

C.    21                         D.    

​[?]​​√​21​​​

​[?]​​√​63​​​

​[?]​​√​147​​​

√​63​​​

√​147​​​

√​21​​​

Write as one root:

3​[?]​​√​7​​​

2√​7​​​

3√​7​​​

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

Solution task 2:

                                       =                         =

3​[?]​​√​7​​​=​[?]​​√​9​​​​[?]​​√​7​​​=​[?]​​√​63​​​

3√​7​​​

√​9​​​⋅√​7​​​

√​63​​​

Above you see the reverse of what we have been doing!

We start with one root and end with

a product of a whole number and a root.

Awesome, is not it?

Another example:

Task 3.  Fill in the 3 numbers in the next slide! So no roots,

just the missing numbers.

The 3 numbers are:

Solution task 3:

The missing numbers are:  

2, 2 and 6.

The complete calculation then is:

​[?]​​√​24​​​=​[?]​​√​4​​​​[?]​​√​6​​​=2​[?]​​√​6​​​

√​24​​​=√​4​​​⋅√​6​​​=2⋅√​6​​​=2√​6​​​

Task 4:

Simplify:

Key in the right answer in the next slide by choosing from:

A.                                B.

C.                                D.

​[?]​​√​48​​​

​[?]​​√​6​​​​[?]​​√​8​​​

6​[?]​​√​8​​​

8​[?]​​√​6​​​

4​[?]​​√​3​​​

√​48​​​

8√​6​​​

4√​3​​​

√​6​​​⋅√​8​​​

6√​8​​​

Simplify:

​[?]​​√​48​​​

1. 8 root 6
2. 4 root 3
3. root 6 root 8
4. 6 root 8

Solution task 4:

Task 5:

Simplify: 

Choose in the next slide from:

A.                                      B.

C.                                      D.

​[?]​​√​243​​​

9​[?]​​√​3​​​

3​[?]​​√​9​​​

81​[?]​​√​3​​​

3​[?]​​√​81​​​

√​234​​​

√​243​​​

3√​9​​​

3√​81​​​

81√​3​​​

9√​3​​​

Task 5: Simplify

​[?]​​√​243​​​

√​243​​​

1. 3 root 9
2. 81 root 3
3. 3 root 81
4. 9 root 3

Solution task 5 - see above.

In this case the root-that-comes-out, 

was maybe hard to find.

Only by practicing this, it will become more easy to find. 

​[?]​​√​81​​​

√​81​​​

Task 6:

Try to SIMPLIFY this:

Simplifying means that the endresult should be:  a number times  a root !

The NEW THING here is the letter p. In the answer it will again turn up as 

Solution in next slide.

​[?]​​√​p​​​

√​p​​​

Solution task 6:

Task 7:

Simplify this expression (answer next slide).

Think about what SIMPLIFYING means! (Finding the highest root that comes out).

Solution 7:

In §9.4 you will need these basic rules for roots:

A few examples about the multiplying of roots first:

Every time you end with one root!

Now with dividing roots:

Again you finally have just one root!

Homework time

Do §9.4 and hand in pics of your work on GoogleClassroom.

Skip:

+ the introduction about areas

+ exercise 30