How do you simplify #sqrt 21 times sqrt 3#?

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Answer 1 · 2016-03-29T13:57:34

#+-3sqrt(7)#

Notice that #3xx7=21#

Write as:#" "sqrt(3xx7)xxsqrt(3)#

This is the same as

#" "sqrt(3)xxsqrt(7)xxsqrt(3)#

Which is the same as

#" "(sqrt(3))^2xxsqrt(7)#

#" "3sqrt(7)#

'~~~~~~~~~~~~~~~~~~~~~~
Note that if #sqrt(3)# is negative then #(sqrt(3))^2# is positive so the 3 is definitely positive.

However, #sqrt(7)# stands on its own so we have #+-sqrt(7)#

Thus #3sqrt(7)" is more correctly written as "+-3sqrt(7)#