What is the square root of 729?

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What is the square root of 729?

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Answer 1 · 2018-05-23T22:32:39

The positive square root is $27$ $27$ and the negative one $- 27$ $-27$ .

Explanation:

First find the prime factorisation of $729$ $729$ :

$000729$ $color(white)(000)729$
$000/0\$ $color(white)(000)"/"color(white)(0)"\"$
$00300243$ $color(white)(00)3color(white)(00)243$
$00000/0\$ $color(white)(00000)"/"color(white)(0)"\"$
$0000300081$ $color(white)(0000)3color(white)(000)81$
$0000000/00\$ $color(white)(0000000)"/"color(white)(00)"\"$
$000000300027$ $color(white)(000000)3color(white)(000)27$
$000000000/00\$ $color(white)(000000000)"/"color(white)(00)"\"$
$00000000300009$ $color(white)(00000000)3color(white)(0000)9$
$000000000000/0\$ $color(white)(000000000000)"/"color(white)(0)"\"$
$0000000000030003$ $color(white)(00000000000)3color(white)(000)3$

So:

$729 = 3^{6}$ $729 = 3^6$

Hence:

$\sqrt{729} = \sqrt{3^{6}} = 3^{3} = 27$ $sqrt(729) = sqrt(3^6) = 3^3 = 27$

This is the positive square root.

$729$ $729$ also has a negative square root $- 27$ $-27$

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What is the square root of 729?

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