Presentation on theme: "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 s s The volume."— Presentation transcript:
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 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
Some Easy Arithmetic First compute the volumes V of cubes with given sides s s V And now answer: What is the cube root of 343?
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.
Now a (much) more difficult question... What is Try to guess! ?
First estimate How big is ? 729 < The greater the side s, the greater the volume V s=9 s=?
Second Estimate Since it is greater than 9, it has at least two. On the other hand: Compute 99 3 = Compare with Since >274625, we have that How many digits has ?
A preliminary result Call a the decimal digit, call b the unit digit. Then We know In other words: has two digits.