Question

How do you find the square root of 405?

Answer 1

`sqrt(405) = 9sqrt(5)`

Explanation:

Taking the prime factors of `405`:

`=3xx135`
`=color(red)(3xx3)xx45`
`=color(red)(3xx3)xx3xx15`
`=color(red)(3xx3)xxcolor(blue)(3xx3)xx5`
`=color(red)(3^2)xxcolor(blue)(3^2)xxcolor(green)(5)`

`sqrt(405)`

`=sqrt(color(red)(3^2)*color(blue)(3^2)*color(green)(5)`
`=sqrt(color(red)(3^2))*sqrt(color(blue)(3^2))*sqrt(color(green)(5))`
`=color(red)(3)*color(blue)(3)*sqrt(color(green)(5))`
`=9sqrt(5)`