How do you find the cube roots $\sqrt[3]{729}$ $root3(729)$ ?

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How do you find the cube roots $\sqrt[3]{729}$ $root3(729)$ ?

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Answer 1 · 2016-11-29T05:20:17

$\sqrt[3]{729} = 9$ $root(3)729=9$

Explanation:

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

$729 = 3 \times 3 \times 81$ $729=3xx3xx81$

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

$729 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3$ $729=3xx3xx3xx3xx3xx3xx3$

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

= $3xx3=9$

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