How do you simplify $(sqrt75-sqrt27)/sqrt12$ ?

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Answer 1 · 2018-03-19T22:49:35

See a solution process below:

First, rewrite each of the radicals as:

$(sqrt(25 * 3) - sqrt(9 * 3))/sqrt(4 * 3)$

Next, use this rule for exponents to simplify each of the radicals:

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

$(sqrt(color(red)(25) * color(blue)(3)) - sqrt(color(red)(9) * color(blue)(3)))/sqrt(color(red)(4) * color(blue)(3)) =>$

$(sqrt(color(red)(25))sqrt(color(blue)(3)) - sqrt(color(red)(9))sqrt(color(blue)(3)))/(sqrt(color(red)(4))sqrt(color(blue)(3))) =>$

$(5sqrt(color(blue)(3)) - 3sqrt(color(blue)(3)))/(2sqrt(color(blue)(3)))$

Next, factor out the common term in the numerator:

$((5 - 3)sqrt(color(blue)(3)))/(2sqrt(color(blue)(3))) =>$

$(2sqrt(color(blue)(3)))/(2sqrt(color(blue)(3))) =>$

$1$

How do you simplify (sqrt75-sqrt27)/sqrt12(sqrt75-sqrt27)/sqrt12?