Question

How do you simplify 5 times square root of 3 plus 4 times square root of 3?

Answer 1

`9sqrt(3)=3^(2.5)`

Explanation:

We have: `5sqrt(3)+4sqrt(3)`.

We know that we can factor this, as `ab+ac=a(b+c)`.

So, we got

`=sqrt(3)(5+4)`

And so, we get

`=9sqrt(3)`

If you want to simplify this further, we can do as follows.

`9=3^2`

So, we have

`=3^2sqrt(3)`

We also know that `sqrt(x)=x^(1/2)`, so we have

`=3^2*3^(1/2)`

We also can use the property that `a^b*a^c=a^(b+c)`, and we got

`=3^(2+1/2)`

`=3^(2 1/2)`

`=3^2.5`

Answer 2

`9*sqrt3`

Explanation:

You have `5*sqrt3+4*sqrt3`.
This can be simplified to `9*sqrt3`.

There are many ways to go about this.
One simple way is to factor out the `sqrt3`:
`5*sqrt3+4*sqrt3`
`= sqrt3(5+4)`
`= sqrt3(9)`
`= 9*sqrt3`

Answer 3

The simplified expression is `9sqrt3`.

Explanation:

First, translate the sentence from English to math:

`stackrel(5) overbrace("5") " " stackrel(xx) overbrace("times") " " stackrel(sqrt3) overbrace("square root of 3") " " stackrel(+) overbrace("plus") " " stackrel(4) overbrace("4") " " stackrel(xx) overbrace("times") " " stackrel(sqrt3) overbrace("square root of 3")`

Now, copy down the expression and simplify it. Since the `sqrt3`'s are like terms, you can add together their coefficients.

`color(white)=5xxsqrt3+4xxsqrt3`

`=color(red)5color(blue)sqrt3+color(red)4color(blue)sqrt3`

`=(color(red)5+color(red)4)color(blue)sqrt3`

`=color(red)9color(blue)sqrt3~~ 15.588457...`

That's as simplified as it gets. Hope this is the answer you were looking for!