How do you express the product of 3[radical 20](2[radical 5] - 7) in simplest radical form?

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Answer 1 · 2016-08-22T10:27:34

#60-42sqrt5#

#color(blue)("Tip about formatting")#
the format command for radical is hash sqrt(20) hash giving #sqrt(2)#.

So you would write: hash 3sqrt(20)(2sqrt(5)-7) hash giving:

# 3sqrt(20)(2sqrt(5)-7)#

Or you could put a space in using "" or color(white)(.)

hash 3sqrt(20) color(white)(.) (2sqrt(5)-7)hash

#" " 3sqrt(20) color(white)(.) (2sqrt(5)-7)#

I wanted the 20 to stand out so I wrote:

hash" " 3sqrt(color(red)(20)) color(white)(.) (2sqrt(5)-7) hash

#" " 3sqrt(color(red)(20)) color(white)(.) (2sqrt(5)-7)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering the question")#

Note that #4xx5=color(red)(20) -> 2^2xx5=color(red)(20)#

#3sqrt(2^2xx5)color(white)(.)(2sqrt(5)-7)#

#3xx2sqrt(5)color(white)(.)(2sqrt(5)-7)#

#6sqrt(5)color(white)(.)(2sqrt(5)-7)#

Note that #6sqrt5xx2sqrt5 = (6xx2)xx(sqrt5color(white)(.))^2 =12xx5#

#(12xx5)-42sqrt(5)#

#60-42sqrt5#