Question

What is the square root of 729?

Answer 1

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

Explanation:

First find the prime factorisation of `729`:

`color(white)(000)729`
`color(white)(000)"/"color(white)(0)"\"`
`color(white)(00)3color(white)(00)243`
`color(white)(00000)"/"color(white)(0)"\"`
`color(white)(0000)3color(white)(000)81`
`color(white)(0000000)"/"color(white)(00)"\"`
`color(white)(000000)3color(white)(000)27`
`color(white)(000000000)"/"color(white)(00)"\"`
`color(white)(00000000)3color(white)(0000)9`
`color(white)(000000000000)"/"color(white)(0)"\"`
`color(white)(00000000000)3color(white)(000)3`

So:

`729 = 3^6`

Hence:

`sqrt(729) = sqrt(3^6) = 3^3 = 27`

This is the positive square root.

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