Math CentralQuandaries & Queries


Question from Alexis, a student:

What would be the square root of 729 to the third power and could you explain how to get the answer?

Hi Alexis,

I think you are looking for $\sqrt[3]{729}$ which is the cube root of $729.$ That is you want the number $a$ so that $a^3 = 729.$

You might be tempted to use the square root button on your calculator, but for an integer like $729$ it's worth the effort to factor it and see if you can deduce the value of $a.$ I'm not going to factor $729$ for you but I'll give you a useful piece of information.

An integer is divisible by 9 if and only if the sum of its digits is divisible by 9.

The sum of the digits of $729$ is $7 + 2 + 9 = 18$ and $18$ is divisible by $9$ so $729$ is divisible by $9.$


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