Question

How do you simplify `sqrt(45n^5)`?

Answer 1

`=3n^2sqrt (5n)`

Explanation:

`sqrt (45n^5`

Prime factorising `45:`

`45 = 3 * 3 * 5 = color(blue)(3^2) * 5`

The expression now becomes:
`sqrt (45n^5) = sqrt ( color(blue)(3^2) * 5 * color(blue)(n ^ 2 * n ^2) * n)`

`=color(blue)(3 * n * n ) sqrt (5n)`

`=3n^2sqrt (5n)`