# How do you simplify #sqrt6(sqrt3+6)#?

##### 1 Answer

#### Explanation:

Yourfirst step is to *expand the paranthesis* by using the distributive property of multiplication.

That is, you can distribute

#color(red)(sqrt(6)) * (sqrt(3) + 6) = color(red)(sqrt(6)) * sqrt(3) + color(red)(sqrt(6)) * 6#

Now, use the *product property of radicals* to write

#sqrt(6) * sqrt(3) = sqrt(6 * 3) = sqrt(18)#

The trick now is to realize that **perfect square** and another number

#18 = 9 * 2 = 3^2 * 2#

This means that the expression can be written as

#sqrt(18) + 6sqrt(6) = sqrt(3^2 * 2) + 6sqrt(6)#

#= sqrt(3^2) * sqrt(2) + 6sqrt(6)#

# = 3sqrt(2) + 6sqrt(6)#

We're not done yet. Notice that you can write

#sqrt(6) = sqrt(2 * 3) = sqrt(2) * sqrt(3)#

This means that the expression becomes

#3sqrt(2) + 6 * sqrt(2) * sqrt(3)#

Use *common factor* to get

#3sqrt(2) + 6 * sqrt(2) * sqrt(3) = color(green)(3sqrt(2) * (1 + 2sqrt(3)))#