How do you simplify #4sqrt18 - 7 sqrt72#?

2 Answers
Aug 5, 2018

#sqrt18=sqrt9sqrt2=3sqrt2#

#sqrt72=sqrt36sqrt2=6sqrt2#

So #4sqrt18-7sqrt72=12sqrt2-42sqrt2=-30sqrt2#

Aug 6, 2018

Answer:

#-30sqrt2#

Explanation:

Since #72=4*18#, we can rewrite #sqrt72# as #sqrt4sqrt72#. We now have

#4sqrt18-7sqrt4sqrt18#

This can be simplified further to

#4sqrt18-14sqrt18#

Next, we can factor out a #sqrt18# to get

#(4-14)sqrt18=-10sqrt18#

Similar to how we simplified #sqrt72#, we can simplify #sqrt18#, rewriting it as #sqrt9sqrt2#. We now have

#-10sqrt9sqrt2#, which simplifies to

#-30sqrt2#

Hope this helps!