How do you multiply #4\sqrt { 2} \cdot 5\sqrt { 14} #?

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Answer 1 · 2017-06-02T20:17:50

See a solution process below:

First, rewrite the expression as:

#(4 * 5)(sqrt(2) * sqrt(14)) => 20(sqrt(2) * sqrt(14))#

Next, use this rule for multiplying radicals:

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

#20(sqrt(color(red)(2)) * sqrt(color(blue)(14))) => 20sqrt(color(red)(2) * color(blue)(14)) => 20sqrt(28)#

We can now use this rule in reverse to simplify the expression:

#20sqrt(28) => 20sqrt(color(red)(4) * color(blue)(7)) => 20(sqrt(color(red)(4)) * sqrt(color(blue)(7))) => 20(2* sqrt(7)) =>#

#40sqrt(7)#

Or

#105.830# rounded to the nearest thousandth.