How do you simplify #-3sqrt45+2sqrt12+3sqrt6-3sqrt20#?

1 Answer
May 26, 2017

Answer:

#=-15sqrt5 +sqrt3(3sqrt2+4)#

Explanation:

#-3sqrt45+2sqrt12+3sqrt6-3sqrt20#

Write the radicands (see below) as the product of their factors, using squares if possible:

#-3sqrt(9xx5)+2sqrt(4xx3)+3sqrt(2xx3)-3sqrt(4xx5)#

Find the roots where possible:

#= -3*3sqrt5 +2*2sqrt3+3sqrt2 sqrt3-3*2sqrt5#

Identify the like terms:

#=color(blue)(-3*3sqrt5-3*2sqrt5" " ) color(red)( +2*2sqrt3+3sqrt2 sqrt3)#

=#color(blue)(-9sqrt5-6sqrt5 )" " color(red)( +4sqrt3+3sqrt2 sqrt3)#

#=-15sqrt5 +sqrt3(3sqrt2+4)#

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#rarr# the word for the value under a root sign is the 'radicand'

#" "sqrt("radicand")#