2Tvwo § 3.5 Cubic roots '19'20

§3.5 Cubic roots

First we look back at §3.4 Simplifying fractions.

Here comes your entrance-ticket!

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Slide 1: Slide

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This lesson contains 20 slides, with interactive quizzes and text slides.

Lesson duration is: 50 min

Items in this lesson

§3.5 Cubic roots

First we look back at §3.4 Simplifying fractions.

Here comes your entrance-ticket!

Slide 1 - Slide

\sqrt ​ 18 ​ ​ ​

timer

0:32

Simplify

Slide 2 - Mind map

solution:

= x = 3 x = 3

\sqrt ​ 18 ​ ​ ​

\sqrt ​ 9 ​ ​ ​

\sqrt ​ 2 ​ ​ ​

\sqrt ​ 2 ​ ​ ​

\sqrt ​ 2 ​ ​ ​

Slide 3 - Slide

\sqrt ​ 72 ​ ​ ​

timer

0:43

Simplify:

Slide 4 - Mind map

Solution:

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

= x = 6 x = 6

\sqrt ​ 72 ​ ​ ​

\sqrt ​ 36 ​ ​ ​

\sqrt ​ 2 ​ ​ ​

\sqrt ​ 2 ​ ​ ​

\sqrt ​ 2 ​ ​ ​

Slide 5 - Slide

§3.5 Cubic roots

We will compare the new thing -Cubic root- with

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

Slide 6 - Slide

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 ​ ​}

Slide 7 - Slide

Slide 8 - Slide

Slide 9 - Slide

A task for the Taskforce (that is YOU!)

ANS

Slide 10 - Slide

The edges are .... cm long.

Slide 11 - Mind map

Slide 12 - Slide

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!

Slide 13 - Slide

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

Slide 14 - Slide

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!

Slide 15 - Slide

Calculate (without a calculator)

​ 3 ​ ​ \sqrt ​ - 1000 ​ ​ ​ =

Slide 16 - Open question

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 ​ ​ \sqrt ​ - 16 ​ ​ ​

​ 3 ​ ​ \sqrt ​ - 16 ​ ​ ​

Slide 17 - Slide

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.

Slide 18 - Slide

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

​ 3 ​ ​ \sqrt ​ 28 ​ ​ ​ \approx

Slide 19 - Open question

Homework Tuesday

Make and correct the exercises from §3.5 (support, standard or challenge).
Finally send in pics of your work in GC again!
you may skip 32

Slide 20 - Slide