Question

How do you simplify `sqrt150 + sqrt 40`?

Answer 1

`5sqrt(6)+2sqrt(10)`

Explanation:

`sqrt(150)+sqrt(40)`
`sqrt(25*6)+sqrt(40)` `color(blue)("Find a factor of 150 that is also a perfect square")`
`5sqrt(6)+sqrt(40)` `color(blue)("Since 25 is a perfect square, pull out a 5")`
`5sqrt(6)+sqrt(10*4)` `color(blue)("Find a factor of 40 that is also a perfect square")`
`5sqrt(6)+2sqrt(10)` `color(blue)("Since 4 is a perfect square, pull out a 2")`

A perfect square is a number that can be pulled out of a radical by multiplying a constant together twice `(5*5=25)`.

`sqrt(6)` and `sqrt(10)` can't be simplified since there are no factors of 6 or 10 that are perfect squares.