2Tvwo § 3.3 Multiplying square roots '19'20

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 2

§3.3 Multiplying square roots

is on the menu today!

However, first there follows a recap on 

adding and subtracting roots!

Write as short as possible

y=3√​x​​​−6√​2​​​+6√​x​​​−2√​2​​​

1. y=9√​x​​​−4√​2​​​
2. y=9√​x​​​−8√​2​​​
3. y=−3√​x​​​+4√​2​​​
4. Cannot be written any shorter.

Which of these does not exist?

1. √​25​​​
2. −√​25​​​
3. √​−25​​​
4. they all exist

Calculate without a calculator

(√​7​​​)​2​​=

Recap

- You cannot take the square root of a negative number

So                               is impossible

- You can only add and subtract square roots with the same number or variable underneath the square root sign. Like:

      

- If you square a square root, you get the number underneath the square root sign (if the square root exists). So for example:

                                   = 7        (this last item is NEW; it's from §3.3 !)

   

√​−6​​​

√​5​​​+3√​5​​​=4√​5​​​

(√​7​[?]​​​​​)​2​​

Multiplying square roots

We've seen that

because: 

 area of the square =               x            =               = 5

As a rule we say:

√​5​​​

√​5​​​

√​25​​​

Let's try to find out if you can multiply roots:

Is this true:

               x                  =                   ?

What does your intuition tell you about this?

ANS

√​4​​​

√​9​​​

√​36​​​

root 9 x root 4 = root 36

1. this is correct
2. not correct

Here you see WHY you can multiply roots:

It is correct to do:

               x                  =                    and this is why:

       2      x      3         =           6 !

As you see, if you rewrite the roots as numbers, the multiplication is correct!

√​4​​​

√​9​​​

√​36​​​

Multiplying square roots

If you multiply different square roots, the following rule applies:

                                                          (if both square roots exist)

Examples:

(

root 3 x root 7 =

1. square root 21
2. square root 10
3. 21

root 18 x root 2 = .....

1. 6
2. square root 36
3. square root 20

explanation:

                                             x                      =                 

This is correct, as you may multiply roots!

However, if possible we have to SIMPLIFY, so the best answer is:

                          = 6 (!), because 6 x 6 = 36

√​18​​​

√​2​​​

√​36​​​

√​36​​​

Homework 

Make and correct §3.3 (support, standard or challenge)

You may skip 16 and 17.

Later on there follows a little more explanation about

exercises 20 and further.

Multiplying square roots

If you multiply square root numbers, the following rule applies:

                                                                         (if both square roots exist)          

Examples:     (take note: in the 2nd one there is NO subtraction!)