How do you evaluate #\sqrt { 45} + 2\sqrt { 20} - 10\sqrt { 5}#?

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Answer 1 · 2017-07-20T00:57:50

See a solution process below:

First, we can rewrite the expression as:

#sqrt(9 * 5) + 2sqrt(4 * 5) - 10sqrt(5)#

Next, use this rule of radicals to simplify the two radicals on the left:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#sqrt(color(red)(9) * color(blue)(5)) + 2sqrt(color(red)(4) * color(blue)(5)) - 10sqrt(5) =>#

#sqrt(color(red)(9))sqrt(color(blue)(5)) + 2sqrt(color(red)(4))sqrt(color(blue)(5)) - 10sqrt(5) =>#

#3sqrt(color(blue)(5)) + (2 * 2)sqrt(color(blue)(5)) - 10sqrt(5) =>#

#3sqrt(5) + 4sqrt(5) - 10sqrt(5)#

Now, factor out the common term of #sqrt(5)# and evaluate:

#(3 + 4 - 10)sqrt(5) =>#

#(7 - 10)sqrt(5) =>#

#-3sqrt(5)#

Which, if necessary, is:

#6.708# rounded to the nearest thousandth.