How do you simplify #7[sqrt3] - 4[sqrt12]#?

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Answer 1 · 2017-05-25T00:16:16

See a solution process below:

First, use this rule of radical multiplication to rewrite the expression:

#sqrt(a * b) = sqrt(a) * sqrt(b)#

#7[sqrt(3)] - 4[sqrt(12)] =>#

#7[sqrt(3)] - 4[sqrt(4 * 3)] =>#

#7[sqrt(3)] - 4[(sqrt(4) * sqrt(3)] =>#

#7[sqrt(3)] - 4[2* sqrt(3)] =>#

#7[sqrt(3)] - 8[sqrt(3)]#

Now, factor a #sqrt(3)# out of each term and combine like terms:

#7[sqrt(3)] - 8[sqrt(3)] =>#

#(7 - 8)[sqrt(3)] =>#

#-1sqrt(3) =>#

#-sqrt(3)#