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42 votes
42 votes
How do you solve this?
(√(3) - √(6) + √(12) -√(24))*(√(6))/(2)

User Mikewied
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1 Answer

17 votes
17 votes


(√(3)-√(6)+√(12)-√(24))\cfrac{√(6)}{2}\qquad \begin{cases} 12=2\cdot 2\cdot 3\\ \qquad 2^2\cdot 3\\ 24=2\cdot 2\cdot\cdot 2 3\\ \qquad 2^2\cdot 6 \end{cases}


(√(3)-√(6)+√(2^2\cdot 3)-√(2^2\cdot 6))\cfrac{√(6)}{2}\implies (√(3)-√(6)+2√(3)-2√(6))\cfrac{√(6)}{2} \\\\\\ (3√(3)-3√(6))\cfrac{√(6)}{2}\implies \cfrac{(3√(3)-3√(6))√(6)}{2}\implies \cfrac{3√(18)-3√(6^2) }{2} \\\\\\ \cfrac{3√(3^2\cdot 2)-3\cdot 6}{2}\implies \cfrac{3\cdot 3√(2)-18}{2}\implies \cfrac{9√(2)-18}{2}\implies \cfrac{9√(2)}{2}-9

User NanoBennett
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