How do you simplify #\frac{25\sqrt{24}}{5\sqrt{2}}#?

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Answer 1 · 2017-11-13T03:09:25

See a solution process below:

First, rewrite the expression as;

#(25/5)(sqrt(24)/sqrt(2)) => 5(sqrt(24)/sqrt(2))#

Next, use this rule of radicals to combine the radicals:

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

#5(sqrt(color(red)(24))/sqrt(color(blue)(2))) => 5sqrt(color(red)(24)/color(blue)(2)) => 5sqrt(12)#

Then, rewrite the term within the radical as:

#5sqrt(4 * 3)#

Now, use this rule for radicals to complete the simplification:

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

#5sqrt(color(red)(4) * color(blue)(3)) => 5sqrt(color(red)(4)) * sqrt(color(blue)(3)) => (5 * 2)sqrt(3) => 10sqrt(3)#