How do you find the cube roots root3(729)?

1 Answer
Shwetank Mauria
Nov 29, 2016

root(3)729=9

Explanation:

Let us first factorize 729 in to rime factors. As sum of digits of 729 is 18, it is divisible by 9 i.e. we can divide it twice by 3. Therefore

729=3xx3xx81

Again 81 is 9^2, hence divisible bt 3 four times more. Hence,

729=3xx3xx3xx3xx3xx3xx3

and root(3)729=root(3)(ul(3xx3xx3)xxul(3xx3xx3))

= 3xx3=9

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