How do you simplify #3sqrt[3] + 2sqrt[27] –sqrt[12]#?

1 Answer
Apr 8, 2016

Answer:

#7sqrt3#

Explanation:

Given an expression to simply
#3sqrt3+2sqrt27-sqrt12#
Factorize second and third terms as

#3sqrt3+2sqrt(3xx3xx3)-sqrt(2xx2xx3#

We know that if there are 2 same digits/numbers under the square root symbol, these can be taken outside the symbol with the condition that the digit/number is written only once outside the symbol. Following this we obtain

#3sqrt3+2xx3sqrt3-2sqrt3#,
simplifying and taking out common factor #sqrt3# gives us
or #3sqrt3+6sqrt3-2sqrt3#
or #sqrt3(3+6-2)#,
simplifying numbers inside the parenthesis we obtain
#7sqrt3#