How do you simplify the expression #sqrt96 div sqrt8#?

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Answer 1 · 2018-05-22T14:18:31

See a solution process below:

First, rewrite the expression as:

#sqrt(96)/sqrt(8)#

Next, use this rule for radicals to start the simplification:

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

#sqrt(color(red)(96))/sqrt(color(blue)(8)) => sqrt(color(red)(96)/color(blue)(8)) => sqrt(12)#

Then, rewrite the term under the radical as:

#sqrt(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))#

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