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:

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

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

How do you simplify the expression sqrt96 div sqrt8sqrt96 div sqrt8?