First we simplify [tex]\sqrt{12}[/tex] :
[tex]\sqrt{12}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex]
This can be simplified further, because [tex]\sqrt{4}[/tex] is just 2:
[tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex] = 2[tex]\sqrt{3}[/tex]
So [tex]\sqrt{12}[/tex] = 2[tex]\sqrt{3}[/tex]
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Now we write 2[tex]\sqrt{3}[/tex] instead of [tex]\sqrt{12}[/tex] in the question:
2[tex]\sqrt{3}[/tex] ( -1 + [tex]\sqrt{5}[/tex])
We solve this by multiplying 2[tex]\sqrt{3}[/tex] by the numbers in the brackets:
2[tex]\sqrt{3}[/tex] ( -1 + [tex]\sqrt{5}[/tex]) = -2[tex]\sqrt{3}[/tex] + 2[tex]\sqrt{15}[/tex]
(Explanation: 2[tex]\sqrt{3}[/tex] × -1 = -2[tex]\sqrt{3}[/tex] , and 2[tex]\sqrt{3}[/tex] × [tex]\sqrt{5}[/tex] = 2[tex]\sqrt{15}[/tex] because the numbers inside of the squares are multiplied by each other - So the 3 times the 5 equals 15)
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Answer:
-2[tex]\sqrt{3}[/tex] + 2[tex]\sqrt{15}[/tex]
(Option B)
