How do you evaluate #\sqrt { 45x } - \sqrt { 108x } + \sqrt { 48x }#?

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Answer 1 · 2017-06-19T07:32:13

#sqrt(3x)(sqrt15-2)#

We cannot evaluate the entire expression unless we have a value for #x#, but we can simplify as far as possible.

First write each radicand as the product of its prime factors - then we know what we are working with.

#sqrt(45x) -sqrt(108x) +sqrt(48x)#

#=sqrt(5*3*3x) -sqrt(2*2*3*3*3x) +sqrt(2*2*2*2*3x)#

Find roots where possible and identify a common factor

#=sqrt(3x)sqrt(3*5) -2*3sqrt(3x) +2*2sqrt(3x)#

Take out the common factor and simplify

#sqrt(3x)(sqrt15-6+4)#