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miah
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\[10\sqrt[4]{6} + 4\sqrt[3]{6} - 9\sqrt[3]{6} - 3\sqrt[4]{6}\]
miah
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@jim_thompson5910
jim_thompson5910
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What are the common terms here
miah
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\[10\sqrt[4]{6} and 3\sqrt[4]{6}\]
miah
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\[4\sqrt[3]{6} and 9\sqrt[3]{6}\]
jim_thompson5910
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good, so combine those pairs of like terms
jim_thompson5910
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for example,
\(\large 10\sqrt[4]{6}\) and \(\large -3\sqrt[4]{6}\)
combine to
\(\large 10\sqrt[4]{6} -3\sqrt[4]{6}\)
\(\large (10 -3)\sqrt[4]{6}\)
\(\large 7\sqrt[4]{6}\)
jim_thompson5910
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how about the other pair of terms? what do they combine to?
miah
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\[-5\sqrt[3]{6}\]
miah
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so the answer is \[7\sqrt[4]{6} - 5\sqrt[3]{6}\]
miah
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@jim_thompson5910
jim_thompson5910
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good you got it
miah
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what about 2√6 ?
miah
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whats also an answer choice.
jim_thompson5910
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you want to simplify this?
miah
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Well it has what i said then my bf said 2√6 and thats also an answer choice.
jim_thompson5910
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oh no it's \[7\sqrt[4]{6} - 5\sqrt[3]{6}\] like you said
miah
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I have another if you dont mind @jim_thompson5910
miah
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\[\sqrt{10} (4-\sqrt{5}) + \sqrt{8} (\sqrt{5}+2)\]
jim_thompson5910
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\[\Large \sqrt{10} (4-\sqrt{5}) + \sqrt{8} (\sqrt{5}+2)\]
\[\Large \sqrt{10} (4)-\sqrt{10} \sqrt{5} + \sqrt{8}\sqrt{5}+\sqrt{8}(2)\]
\[\Large 4\sqrt{10}-\sqrt{10*5} + \sqrt{8*5}+2\sqrt{8}\]
\[\Large 4\sqrt{10}-\sqrt{50} + \sqrt{40}+2\sqrt{8}\]
\[\Large 4\sqrt{10}-\sqrt{25*2} + \sqrt{4*10}+2\sqrt{4*2}\]
\[\Large 4\sqrt{10}-\sqrt{25}*\sqrt{2} + \sqrt{4}*\sqrt{10}+2\sqrt{4}\sqrt{2}\]
\[\Large 4\sqrt{10}-5\sqrt{2} + 2\sqrt{10}+2*2\sqrt{2}\]
\[\Large 4\sqrt{10}-5\sqrt{2} + 2\sqrt{10}+4\sqrt{2}\]
\[\Large 6\sqrt{10}-\sqrt{2}\]
miah
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Thank youuu!
miah
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\[\frac{ 2 }{ 6-\sqrt{3} } \]
miah
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Last one i Promise. lol
miah
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@jim_thompson5910
jim_thompson5910
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multiply top and bottom by \(\Large 6+\sqrt{3}\) and tell me what you get
miah
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12 over √ 3
jim_thompson5910
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no you should get this
jim_thompson5910
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\[\Large \frac{ 2 }{ 6-\sqrt{3} } \]
\[\Large \frac{ 2(6+\sqrt{3}) }{ (6-\sqrt{3})(6+\sqrt{3}) } \]
\[\Large \frac{ 2(6+\sqrt{3}) }{ 6^2 - \left(\sqrt{3}\right)^2 } \]
\[\Large \frac{ 2(6+\sqrt{3}) }{ 36 - 3 } \]
\[\Large \frac{ 2(6+\sqrt{3}) }{ 33 } \]
\[\Large \frac{ 12+2\sqrt{3} }{ 33 } \]
miah
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Thanks!