How do you simplify 4 sq.root of 75 + sq.root of 27.?

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Answer 1 · 2015-07-13T15:03:13

#4sqrt75+sqrt27=23sqrt3#

We are given:

#4sqrt75+sqrt27#

Let's look at #sqrt75#

#25# goes into #75# #3# times

#3*25=75#

So,

#sqrt75=sqrt(3*25)#

the square root of #25# is #5#, so

#sqrt75=sqrt(3*25)=5sqrt3#

Now, let's look at #sqrt27#

#3# goes into #27# #9# times

#3*9=27#

So,

#sqrt27=sqrt(3*9)#

the square root of #9# is #3#, so

#sqrt27=sqrt(3*9)=3sqrt3#

So,

#4sqrt75+sqrt27=4*5sqrt3+3sqrt3#

#4*5sqrt3+3sqrt3=20sqrt3+3sqrt3=23sqrt3#

Recall: #asqrtb+csqrtb=(a+c)sqrtb#

Answer 2 · 2015-07-13T15:04:01

#4sqrt(75)+sqrt(27)=23sqrt(3)#

Use #sqrt(ab) = sqrt(a)sqrt(b)# for #a, b >= 0#

#4sqrt(75)+sqrt(27)#

#=4sqrt(5^2*3)+sqrt(3^2*3)#

#=4sqrt(5^2)sqrt(3)+sqrt(3^2)sqrt(3)#

#=4*5sqrt(3)+3sqrt(3)#

#=20sqrt(3)+3sqrt(3)#

#=23sqrt(3)#