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Let’s play a game! . }. =?. =?. =?. Guess cube roots. Recall: What is a Cube Root?. The edges of a cube all have the same measure: let’s call it s . s. The volume V of this cube is then given by the formula. s. s. We can also write. V = s 3. s = 3 V. We say that

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let s play a game

Let’s play a game!

}

=?

=?

=?

Guess cube roots

recall what is a cube root
Recall: What is a Cube Root?
  • The edges of a cube all have the same measure: let’s call it s.

s

  • The volume V of this cube is then given by the formula

s

s

We can also write

V = s3

s = 3V

We say that

V is the cube of s

and say that

s is the cube root of V

some easy arithmetic
Some Easy Arithmetic

First compute the volumes V of cubes with given sides s

s 1 2 3 4 5 6 7 8 9

V 1 8 27 64 125 216 343 512 729

What is the cube root of 343?

And now answer:

answer
Answer!
  • The cube root of 343 is 7, i.e.,

V = 343

In other words:

  • The side of a cube of volume V = 343 is s = 7.

s = 7

first estimate
First estimate

How big is ?

274625

The greater the side s,the greater the volume V

729

s=9

s=?

<

second estimate
Second Estimate

How many digits has ?

Since it is greater than 9, it has at least two.

On the other hand:

Compute 993 = 970299.

Compare 970299 with 274625.

Since 970299 >274625, we have that

find a b
Find a, b!

Solve the equation:

274625

=

10 a

b

expand the cubic expression
Expand the Cubic Expression

10a*10a*b =

100a2b

10a*b

*b =

10ab2

10a*b*b =

10ab2

b*

b*b

=b3

10a*10a*b=

100a2b

10a *

10a

*b=

100a2b

10a*10a*

10a=

1000a3

10a *

b*

b=

10ab2

summing up

3* 2 *

3

3* * 2

3

Summing up!

100a2b

100a2b

1000a3

10ab2

10ab2

100a2b

10ab2

b3

1000a3

3*100a2b

3*10ab2

b3

Compare with the formula for cubic expressions:

step 1

10a*10a*b =

100a2b

b*

b *10a =

10ab2

10a*b*b =

10ab2

b*

b*b

=b3

10a*10a*b=

100a2b

b*

10a *

10a=

100a2b

(10a)3=

1000a3

b*

10a *

b=

10ab2

274625

Step 1:

is a perfect cube close to

1000a3

equivalently
Equivalently:

Divide by 1000 and find a cube

close to

Answer:

Hence:

step 2

100a2b

10a*10a*b =

100a2b

b*

b *10a =

10ab2

10a*b*b =

10ab2

b*

b*b

=b3

100a2b

10a*10a*b=

100a2b

b*

10a *

10a=

100a2b

100a2b

b*

10a *

b=

10ab2

58625

Step 2:

from

Subtract

.

and obtain

Approximate it with

in other words
In other words:

by

Divide

and find the quotient

Conclusion:

Right guess?

slide17

And now…

try again!

Good luck!