Question

FINAL REVIEW HELP : sqrt{6}(7sqrt{12}- 10sqrt{3})

Answer 1

√ 12 = √ (4 * 3 ) = ...

Answer 2

\[12\sqrt{2}\] ?

Answer 3

4 = 2²

Answer 4

√ 12 = √ (4 * 3 )
= √ 2² * √ 3
= ...

Answer 5

I would distribute the sqrt(6)
I would factor all the numbers under the radical sign

\[ \sqrt{6}(7\sqrt{12}- 10\sqrt{3})\]
\[ (7\sqrt{12}\sqrt{6}- 10\sqrt{3}\sqrt{6})\]
\[ (7\sqrt{12 \cdot 6}- 10\sqrt{3\cdot 6})\]
now factor 12 into \(2\cdot 2 \cdot 3 \) and 6 into \(2\cdot 3 \)
\[ (7\sqrt{2\cdot 2 \cdot 3 \cdot 2 \cdot 3}- 10\sqrt{3\cdot 2 \cdot 3})\]
now pull out "pairs" from out of the radical
\[ (7\cdot 2 \cdot 3\sqrt{2 }- 10\cdot 3\sqrt{ 2 })\]

now simplify. what do you get?

Answer 6

\[42\sqrt{2}-10\sqrt{3}\]