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

2 Answers
Oct 4, 2017

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

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)