How do you simplify #3sqrt20 + 5sqrt45 + sqrt75#?

2 Answers
Mar 31, 2017

Answer:

#3sqrt20+5sqrt45+sqrt75=21sqrt5+5sqrt3#

Explanation:

A square root can be simplified by looking for a square number that's a factor of the number within a square root. We use the rule #sqrt(ab)=sqrta*sqrtb# to simplify square roots.

Looking at just the first term, we see that we have #sqrt20#. This can be simplified by noticing that #20=4xx5#, and #4=2^2#. Then, we can say that #sqrt(20)=sqrt(4xx5)=sqrt4sqrt5=2sqrt5#.

We can follow this logic for all the square roots:

#3sqrt20+5sqrt45+sqrt75#

#=3sqrt(4xx5)+5sqrt(9xx5)+sqrt(25xx3)#

#=3sqrt4sqrt5+5sqrt9sqrt5+sqrt25sqrt3#

#=3(2)sqrt5+5(3)sqrt5+5sqrt3#

#=6sqrt5+15sqrt5+5sqrt3#

The terms that both contain #sqrt5# can be simplified. This is analogous to doing #6x+15x=21x#:

#=21sqrt5+5sqrt3#

Mar 31, 2017

Answer:

#21 sqrt(5) + 5 sqrt(3)#

Explanation:

#3 sqrt(20) = 3 sqrt(4*5) = 3*2 sqrt(5) = 6 sqrt(5)#
#5 sqrt(45) = 5 sqrt(9*5) = 5*3 sqrt(5) = 15 sqrt(5)#
#sqrt(75) = sqrt(25*3) = 5 sqrt(3)#