First, rewrite each of the radicals as:
(sqrt(25 * 3) - sqrt(9 * 3))/sqrt(4 * 3)√25⋅3−√9⋅3√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))√a⋅b=√a⋅√b
(sqrt(color(red)(25) * color(blue)(3)) - sqrt(color(red)(9) * color(blue)(3)))/sqrt(color(red)(4) * color(blue)(3)) =>√25⋅3−√9⋅3√4⋅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))) =>√25√3−√9√3√4√3⇒
(5sqrt(color(blue)(3)) - 3sqrt(color(blue)(3)))/(2sqrt(color(blue)(3)))5√3−3√32√3
Next, factor out the common term in the numerator:
((5 - 3)sqrt(color(blue)(3)))/(2sqrt(color(blue)(3))) =>(5−3)√32√3⇒
(2sqrt(color(blue)(3)))/(2sqrt(color(blue)(3))) =>2√32√3⇒
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