2Tvwo § 3.5 Cubic roots '19'20

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§3.5 Cubic roots

First we look back at §3.4 Simplifying fractions.

Here comes your entrance-ticket!

√​18​​​

Simplify

solution:

=              x                    =        3     x                      =   3  

  

√​18​​​

√​9​​​

√​2​​​

√​2​​​

√​2​​​

√​72​​​

Simplify:

Solution:

There are more possibilities, but we always search for the LARGEST square root. So:

                                 =                x              =   6  x               =    6

     

√​72​​​

√​36​​​

√​2​​​

√​2​​​

√​2​​​

§3.5 Cubic roots

We will compare the new thing -Cubic root- with 

the Square root, that is well-known to you by now!

Cubic roots

We could think of square roots

as the length of the sides of a

square if you know the area.

In the same way, cubic roots

can be thought of as the length of the sides of 

a cube if you know the volume.                                 Volume cube    = 3 x 3 x 3 

                                                                                                                                      = 27   

3​3​​

A task for the Taskforce (that is YOU!)

ANS

The edges are .... cm long.

Once more: a cubic root belongs to a cube!

When you know the volume, then the length, width and height are 

the cubic root of the volume!

Watch this big difference between square roots and cubic roots:

√(-100)        does not exist, because there is no number that, when squared,

becomes -100.     However ...........

∛(-1000)  DOES exist!      

Because:             -10 x -10 x -10 = -1000

So the Cubic Root of -1000 is -10.                                                             

Or:    ∛(-1000) = -10    

Cubic roots

Unlike square roots, it is possible to take the cubic root of a negative number, because a negative number raised to the third power is negative!

Calculate (without a calculator)

​3​​√​−1000​​​=

Exact or approximation

If you try to calculate                  on your calculator

(use shift + the button shown on the right)

you will get the result -2.5198421

This number is an approximation to 7 decimal places.

If you round off to -2.52 it is an approximation to

2 decimal places.

                   is an exact value.

​3​​√​−16​​​

​3​​√​−16​​​

This KEY you need to use:

Key in:

SHIFT + the key

shown here.

Then you take the

CUBIC ROOT or

THIRD ROOT

of 64, which is 4.

Use your calculator to give an approximation accurate to 3 decimal places of

​3​​√​28​​​≈

Homework Tuesday

• Make and correct the exercises from §3.5 (support, standard or challenge).
• Finally send in pics of your work in GC again!
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