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

1 Answer
May 26, 2017

=-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")