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Simplify: (√6−2√3)2(√6-2√3)^2(√6−2√3)2​​
Question

Simplify: (623)2(√6-2√3)^2​​

A.

18+2√12

B.

18-2√12

C.

18+12√2

D.

18-12√2

Correct option is D

Given:  

(623)2(√6-2√3)^2 

Solution:  

As we know,=>(ab)2=a2+b22ab=>(623)2=>(6)2+(23)22×6×23=>6+12418=>18122\text{As we know,} \\ \Rightarrow (a - b)^2 = a^2 + b^2 - 2ab \\ \Rightarrow (\sqrt{6} - 2\sqrt{3})^2 \\ \Rightarrow (\sqrt{6})^2 + (2\sqrt{3})^2 - 2 \times \sqrt{6} \times 2\sqrt{3} \\ \Rightarrow 6 + 12 - 4 \sqrt{18} \\ \Rightarrow 18 - 12\sqrt{2}​​


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