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

3 Answers
Mar 14, 2018

Answer:

#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#

Mar 14, 2018

Answer:

#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#

Mar 14, 2018

Answer:

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!