Answer :
The fully simplified expression is 54[tex]\sqrt{2}[/tex] - 2[tex]\sqrt{3}[/tex].
The correct answer is option E.
Given expression: [tex]\sqrt{6}[/tex] * 2[tex]\sqrt{3}[/tex] * [tex]\sqrt{27}[/tex] - [tex]\sqrt{12}[/tex]
Simplify [tex]\sqrt{27}[/tex] to get 3[tex]\sqrt{3}[/tex]:
[tex]\sqrt{6}[/tex]* 2[tex]\sqrt{3}[/tex] * 3[tex]\sqrt{3}[/tex]- [tex]\sqrt{12}[/tex]
Simplify [tex]\sqrt{6}[/tex]* 2[tex]\sqrt{3}[/tex] to get 2[tex]\sqrt{18}[/tex]:
2[tex]\sqrt{18}[/tex] * 3[tex]\sqrt{3}[/tex]- [tex]\sqrt{12}[/tex]
Simplify sqrt(18) to get ([tex]\sqrt{9 * 2}[/tex]):
2([tex]\sqrt{9 * 2}[/tex]):* 3[tex]\sqrt{3}[/tex] - [tex]\sqrt{12}[/tex]
Further simplify ([tex]\sqrt{9 * 2}[/tex]):to get 3[tex]\sqrt{2}[/tex]:
2 * 3[tex]\sqrt{2}[/tex] * 3[tex]\sqrt{3}[/tex] - [tex]\sqrt{12}[/tex]
Simplify 2 * 3[tex]\sqrt{2}[/tex] to get 6[tex]\sqrt{2}[/tex]:
6[tex]\sqrt{2}[/tex] * 3[tex]\sqrt{3}[/tex]- [tex]\sqrt{12}[/tex]
Simplify [tex]\sqrt{12}[/tex] to get 2[tex]\sqrt{3}[/tex]:
6[tex]\sqrt{2}[/tex] * 3[tex]\sqrt{3}[/tex]- 2[tex]\sqrt{3}[/tex]
Distribute and multiply:
18[tex]\sqrt{6}[/tex] [tex]\sqrt{3}[/tex] - 2[tex]\sqrt{3}[/tex]
Simplify [tex]\sqrt{6}[/tex] [tex]\sqrt{3}[/tex] to get [tex]\sqrt{18}[/tex]:
18[tex]\sqrt{18}[/tex] - 2[tex]\sqrt{3}[/tex]
Simplify [tex]\sqrt{18}[/tex] to get 3[tex]\sqrt{2}[/tex]:
18 * 3[tex]\sqrt{2}[/tex] - 2[tex]\sqrt{3}[/tex]
Multiply and combine like terms:
54[tex]\sqrt{2}[/tex] - 2[tex]\sqrt{3}[/tex]
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The question probable may be:
Which choice is equivalent to the expression below?
[tex]\sqrt{6}[/tex] * 2[tex]\sqrt{3}[/tex] *[tex]\sqrt{27}[/tex]- [tex]\sqrt{12}[/tex]
A. 3[tex]\sqrt{3}[/tex]+ [tex]\sqrt{6}[/tex]
B. 5[tex]\sqrt{3}[/tex]
C. 5[tex]\sqrt{3}[/tex] - 6
D. 2[tex]\sqrt{3}[/tex]- [tex]\sqrt{21}[/tex]
E. none of them