How do you solve #\frac { \sqrt { 12} \times \sqrt { 3} } { 2} + \frac { \sqrt { 128} } { \sqrt { 2} } #?

1 Answer
smendyka
Oct 18, 2017

See a solution process below:

Explanation:

First, multiply the fraction on the right by the appropriate form of #1# to put both fractions over a common denominator:

#(sqrt(12) xx sqrt(3))/2 + (sqrt(128)/sqrt(2) xx sqrt(2)/sqrt(2)) =>#

#(sqrt(12) xx sqrt(3))/2 + (sqrt(128) xx sqrt(2))/sqrt(2)^2 =>#

#(sqrt(12) xx sqrt(3))/2 + (sqrt(128) xx sqrt(2))/2#

Next, use these rules for radicals to simplify each of the numerators:

#sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))# and #sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#sqrt(12 xx 3)/2 + sqrt(128 xx 2)/2 =>#

#sqrt(36)/2 + sqrt(256)/2 =>#

#6/2 + 16/2 =>#

#22/2 =>#

#11#

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