Question

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

Answer 1

`=-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")`