How do you simplify #-2\sqrt { 18} - 2\sqrt { 54} - 4\sqrt { 6}#?

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Answer 1 · 2018-01-01T02:35:15

#-2sqrt18-2sqrt54-4sqrt6=#

#-6sqrt2-10sqrt6=#

#-2(3sqrt2+5sqrt6)#

depending on whether you factor the answer completely.

Simplify:

#-2sqrt18-2sqrt54-4sqrt6#

You can only add or subtract numbers with the same square root.

Prime factorize each square root.

#-2sqrt(2xx3^2)-2sqrt(2xx3xx3^2)-4sqrt(2xx3)#

Simplify the radicals.

#-2xx3sqrt2-2xx3sqrt6-4sqrt6#

Collect like terms.

#-6sqrt2+(-6sqrt6-4sqrt6)#

Simplify.

#-6sqrt2-10sqrt6#

Factor out the common #-2#.

#-2(3sqrt2+5sqrt6)#