Answer:
√3
Step-by-step explanation:
The given expression to be simplified is
[tex]2 \sqrt{27}+\sqrt{12}-3\sqrt{3}-2 \sqrt{12}[/tex]
but
[tex]2 \sqrt{27}=2\sqrt{9 \times 3}=2 \times \sqrt{9}\times \sqrt{3}=2 \times 3 \times\sqrt{3}=6 \sqrt{3} [/tex]
[tex] \sqrt{12}=\sqrt{4\times3}= \sqrt{4}\times \sqrt{3}=2\sqrt{3} [/tex]
Since √12=2√3,this implies that,
[tex]2\sqrt{12}=2\times2\sqrt{3}=4 \sqrt{3} [/tex]
Therefore,
[tex]2 \sqrt{27}+\sqrt{12}-3\sqrt{3}-2 \sqrt{12}=6\sqrt{3}+2\sqrt{3}-3 \sqrt{3} -4\sqrt{3} [/tex]
[tex] =(6+2-3-4)\sqrt{3} [/tex]
[tex] =\sqrt{3} [/tex]
The simplified form of ,
[tex]2 \sqrt{27}+\sqrt{12}-3\sqrt{3}-2 \sqrt{12}[/tex] is √3
