How do you simplify #3sqrt27+4sqrt12-sqrt300#?

2 Answers
Oct 4, 2017

Answer:

#7sqrt3#

Explanation:

#3sqrt27+4sqrt12-sqrt300#

#=3sqrt(9xx3)+4sqrt(4xx3)-sqrt(100xx3)#
#=3sqrt9sqrt3+4sqrt4sqrt3-sqrt100sqrt3#
#=(3xx3)sqrt3+(4xx2)sqrt3-10sqrt3#
#=9sqrt3+8sqrt3-10sqrt3#
#=17sqrt3-10sqrt3#
#=7sqrt3#

Oct 4, 2017

Answer:

#3sqrt(27)+4sqrt(12)-sqrt(300)=7sqrt(3)#

Explanation:

To answer this question, you need to get each number to the same root. You cannot do anything with them now, but by giving them a square root in common you can simplify this expression.

This is best worked out by splitting each part of the expression up:

#3sqrt(27)=3sqrt(9*3)=3*sqrt(9)*sqrt(3)=3*3*sqrt(3)=9sqrt(3)#

In short, #3sqrt(27)=9sqrt(3)#

Similarly,

#4sqrt(12)=4sqrt(4*3)=4*sqrt(4)*sqrt(3)=4*2*sqrt(3)=8sqrt(3)#

In short, #4sqrt(12)=8sqrt(3)#

And then again:

#sqrt(300)=sqrt(100*3)=sqrt(100)*sqrt(3)=10*sqrt(3)=10sqrt(3)#

In short, #sqrt(300)=10sqrt(3)#

Putting these together we get:
#9sqrt(3)+8sqrt(3)-10sqrt(3)#
#=7sqrt(3)#