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Simplify completely: 2 square root 3 - square root 6 all over 3 square root 6 + 2 square root 3

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asked Dec 7, 2016 48.1k views

5 votes

Simplify completely: 2 square root 3 - square root 6 all over 3 square root 6 + 2 square root 3

Mathematics
high-school

Benjamin Muschko asked

by Benjamin Muschko

7.9k points

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1 Answer

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$(2\sqrt3-\sqrt6)/(3\sqrt6+2\sqrt3)=\\ ((2\sqrt3-\sqrt6)(3\sqrt6-2\sqrt3))/((3\sqrt6+2\sqrt3)(3\sqrt6-2\sqrt3))=\\ (6√(18)-12-18+2√(18))/(54-12)=\\ (-30+8√(18))/(42)=\\ (-30+24√(2))/(42)=\\ (-5+4√(2))/(7)$

Chrispytoes answered Dec 13, 2016

by Chrispytoes

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Simplify completely: 2 square root 3 - square root 6 all over 3 square root 6 + 2 square root 3

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