Download presentation

Presentation is loading. Please wait.

Published byRuben Mescall Modified over 2 years ago

1
Let’s play a game! Guess cube roots } =?

2
Recall: What is a Cube Root? The edges of a cube all have the same measure: let’s call it s. s s s The volume V of this cube is then given by the formula V = s 3 We say that V is the cube of s We can also write s = 3 V and say that s is the cube root of V

3
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 And now answer: What is the cube root of 343?

4
Answer! The cube root of 343 is 7, i.e., V = 343 s = 7 In other words: The side of a cube of volume V = 343 is s = 7.

5
Now a (much) more difficult question... What is Try to guess! ?

6
First estimate 274625 How big is ? 729 < The greater the side s, the greater the volume V s=9 s=?

7
Second Estimate Since it is greater than 9, it has at least two. On the other hand: Compute 99 3 = 970299. Compare 970299 with 274625. Since 970299 >274625, we have that How many digits has ?

8
A preliminary result Call a the decimal digit, call b the unit digit. Then We know In other words: has two digits.

9
Find a, b! 274625 10 a b Solve the equation: =

10
10a*10a*b= 100a 2 b Expand the Cubic Expression 10a*10a* 10a= 1000a 3 10a * 10a *b= 100a 2 b 10a*10a*b = 100a 2 b 10a*b*b = 10ab 2 10a * b* b= 10ab 2 10a*b *b = 10ab 2 b*b*b=b3 b*b*b=b3

11
Summing up! 1000a 3 100a 2 b 10ab 2 b 3 1000a 3 3*100a 2 b3*10ab 2 b3b3 Compare with the formula for cubic expressions: 3* 2 * 3 3* * 2 3

12
Step 1: is a perfect cube close to 1000a 3 10a*10a*b= 100a 2 b 10a*10a*b = 100a 2 b (10a) 3 = 1000a 3 10a*b*b = 10ab 2 b* 10a * 10a= 100a 2 b b* b *10a = 10ab 2 b* 10a * b= 10ab 2 b* b*b =b 3 274625

13
Equivalently: Divide by 1000 and find a cube close to Answer: Hence:

14
Step 2: Subtract from 100a 2 b Approximate it with and obtain 10a*10a*b= 100a 2 b 10a*10a*b = 100a 2 b 10a*b*b = 10ab 2 b* 10a * 10a= 100a 2 b b* b *10a = 10ab 2 b* 10a * b= 10ab 2 b* b*b =b 3 58625.

15
In other words: Divide by Conclusion: and find the quotient Right guess?

16
Let’s check! Right!

17
And now… Good luck! try again!

Similar presentations

OK

1-4 Powers and Exponents Warm Up Lesson Presentation Lesson Quiz

1-4 Powers and Exponents Warm Up Lesson Presentation Lesson Quiz

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Free ppt on mobile number portability process Ppt on business environment nature concept and significance definition Ppt on clutch system in automobile Ppt on number system in maths Ppt on class ab power amplifier Ppt on art and craft movement Ppt on rutherford's gold foil experiment Ppt on recycling of solid waste Upload and view ppt online reader Ppt on 2nd world war movies