Question

How do you simplify `sqrt(3a) + 2sqrt(27a^3)`?

Answer 1

`sqrt(3a)+2sqrt(27a^3)=color(green)((1+6a)(sqrt(3a))`

Explanation:

`2sqrt(27a^3)=2*sqrt(3^2*2*a^2*a)`
`color(white)("XXX")=2*sqrt((3a)^2)*sqrt(3a)`
`color(white)("XXX") =6asqrt(3a)`

So
`sqrt(3a)+2sqrt(27a^3)`
`color(white)("XXX")=sqrt(3a)+6asqrt(3a)`
`color(white)("XXX")=(1+6a)sqrt(3a)`

Answer 2

`sqrt(3a)(6a+1)`

Explanation:

Notice that `3xx9=27->3xx3^3=27`
Also notice that `a^3=a^2xxa`

Write as:
`sqrt(3a)+2sqrt(3^2a^2xx3a)`

Take the `3^3a^a` outside the square root as `sqrt(3^2a^2)=3a`

`sqrt(3a)+(3axx2xxsqrt(3a))`

`sqrt(3a)+6asqrt(3a)`

Factor out the `sqrt(3a)`

`sqrt(3a)(1+6a)`

Or if you prefer

`sqrt(3a)(6a+1)`