How do you multiply #-7\sqrt { 89} \cdot - 5\sqrt { 176q }#?

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Answer 1 · 2017-06-06T01:36:31

See a solution process below:

First, rewrite this expression as:

#(-7 * -5)(sqrt(89) * sqrt(176q)) = 35(sqrt(89) * sqrt(176q))#

We can 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)(89)) * sqrt(color(blue)(176q))) = 35sqrt(color(red)(89) * color(blue)(176q)) = 35sqrt(15664q)#

We can then rewrite this expression as:

#35sqrt(15664q) = 35sqrt(16 * 979q)#

We can now rewrite the radical using the rule above in reverse:

#35sqrt(16 * 979q) = 35sqrt(16)sqrt(979q) = (35 * 4)sqrt(979q) =#

#140sqrt(979q)#