karinewoods17
combine {sqrt -8} + {sqrt -32}
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karinewoods17
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The answer in my book is \[6i - 2i \sqrt{10}\] I dont know how they got that answer.
ilikephysics2
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You can't take the square root of a negative number
ChmE
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@ksaimouli is incorrect
karinewoods17
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thats why you multiply it by i which is equal to -1
Ahaanomegas
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@ksaimouli That's totally wrong. sqrt(a)+sqrt(b) is NOT sqrt(a+b).
@ilikephysics2 Yes, You can. That's what imaginary numbers are there for.
@karinewoods17 Notice that \[ \Large {\sqrt {8} = 2\sqrt{2}} \]and \[ \Large {\sqrt {32} = 4\sqrt{2}}, \]so \[ \Large {\sqrt {-8} = 2i\sqrt{2}} \]and \[ \Large {\sqrt {-32} = 4i\sqrt{2}} \]Do you see how that works? Now, just add to get 6isqrt(2).
karinewoods17
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wouldnt it be \[6i \sqrt{2}\] ??
ChmE
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\[\sqrt{-8}+\sqrt{-32}=\sqrt{-8}+\sqrt{-8\times4}= \sqrt{-8} + 2\sqrt{-8}\]
ChmE
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\[3\sqrt{-8}=3i \sqrt{8}=3i \sqrt{2\times4}=6i \sqrt{2}\]
ChmE
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Yes you are correct
Ahaanomegas
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Yep. That's exactly what I said, except I explained everything. =P
karinewoods17
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but... the answer in my book says the answer is \[6i - 2i \sqrt{10}\] How did they get that?
karinewoods17
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Im sorry:/ Im making coffee and waiting for you:)
karinewoods17
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im not! sorry!
karinewoods17
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I was making breakfast for my boyfriend.
karinewoods17
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umm. \[\sqrt{-32}\] breaks into \[\sqrt{-32} = \sqrt{4} * \sqrt{-8}\] which simplifies to \[4i \sqrt{2}\] ?
karinewoods17
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And yes I try:)
karinewoods17
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now what. lol
karinewoods17
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@nincompoop please do not ignore me;)