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What to the third power is equal to 729

User Jumble
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2 Answers

6 votes
9 to the third power is equal to 729. 9x9x9 = 729.
User Bjarte Aune Olsen
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8.3k points
5 votes

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.)
User Alelom
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