How do you multiply #7\sqrt { 11} \cdot 5\sqrt { 12}#?

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Answer 1 · 2018-01-16T21:56:52

See a solution process below:

First, rewrite the expression as:

#(7 * 5)(sqrt(11) * sqrt(12)) =>#

#35(sqrt(11) * sqrt(12))#

Next, use this rule for multiplying radicals:

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

#35(sqrt(color(red)(11)) * sqrt(color(blue)(12))) =>#

#35sqrt(color(red)(11) * color(blue)(12)) =>#

#35sqrt(132)#

Then, we can rewrite the term in the radical as:

#35sqrt(color(red)(4) * color(blue)(33))#

We can now use the opposite of the rule above to simplify the radical:

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

#35sqrt(color(red)(4) * color(blue)(33)) =>#

#35sqrt(color(red)(4)) * sqrt(color(blue)(33)) =>#

#(35 * 2)sqrt(color(blue)(33)) =>#

#70sqrt(33)#