Mathematics

# What to the third power is equal to 729

### Answers

#### Abbiejolliff

3 years ago

If you had absolutely no idea, then you'd have roughly two choices
of how to find it:

#1).  Try numbers until you find the right one.

Pick a number.
Cube it.
If you get less than 729, go back and try a bigger number.
If you get more than 729, go back and try a smaller number.
Eventually you find the right one.

Try 1.        1³ = 1 .            Too small.
Try 2.        2³ = 8 .            Still too small.
Try 5.        5³ = 125 .        Still too small.
Try 20.     20³ = 8,000.      Ooops.  Too big.
Try 10.     10³ = 1,000       Too big.
Try 8.         8³ = 512.         Oooo.  Too small, but maybe getting close.
Try 8.5.    8.5³ = 614.125   Still too small, but very close.
Try 9.         9³ = 729 .       That's it !            yay !

#2).  x³ = 729

Take the log of each side:      log(x³) = log(729)

3 log(x)  =  log(729)

Divide each side by  3 :         log (x)  =  (1/3) log(729)

Look up log(729) :                 log(x)  =  (1/3) (2.86272...)

=    0.95424...
Raise 10 to the power
of each side:                      10^log(x)  =  10⁰·⁹⁵⁴²⁴···

x        =  8.99994...

(That's the way it is with logs.
They never come out even.)

#### Madtown

3 years ago

9 to the third power is equal to 729. 9x9x9 = 729.