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This is confusing...
Topic Started: Feb 18 2011, 07:49 PM (320 Views)
Michelle
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.

After I had clicked on "help me solve this" and finished it, I should have written down better instructions.

The example was

6√27 - 2√18 + 75

Which equals

6√9 · 3 - 2√9 · 2 + 3√25

Which equals

6 · √9 · √3 - 2 · √9 · √2 + √25 · 3

Which equals

18 · √3 - 6 · √2 + 5√3

Which equals

18 · √3 - 6 · √2 + 5√3

Which equals

18√3 - 6√2 + 5√3

Which equals

(18 + 5)√3 - 6√2

Which equals

23√3 - 6√2




Here's the question I'm on:

6√48 - 2√32 + √27 =

6√6 · 8 + 2√8 · 4 + 3√9

So yeah... I'm stuck on the third step :(
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CJ
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A very minor case of serious brain damage

OK, so, we're starting with "6√48 - 2√32 + √27". What you need to do is re-write each of the numbers being square rooted as the product of two numbers, one of which should be a square number. So, 48 = 16 · 3; 32 = 16 · 2; 27 = 9 · 3. Substituting those in:

6√48 - 2√32 + √27 = 6√(16 · 3) - 2√(16 · 2) + √(9 · 3)

Now, square roots distribute across multiplication:

6√(16 · 3) - 2√(16 · 2) + √(9 · 3) = 6(√16)(√3) - 2(√16)(√2) + (√9)(√3)

But, √16 is just 4, and √9 is just 3:

6(√16)(√3) - 2(√16)(√2) + (√9)(√3) = 6 · 4√3 - 2 · 4√2 + 3√3 = 24√3 - 8√2 + 3√3 = 27√3 - 8√2

So, the answer is 27√3 - 8√2.

Hope that helped!
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Michelle
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It was right! Thank you so much!
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CJ
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A very minor case of serious brain damage

You're welcome :) . Just ask again if you need any more help.
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Michelle
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Okay. I will. I may reply again, if need be.
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CJ
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A very minor case of serious brain damage

In case it helps, here are some common ones:

√8 = 2√2
√12 = 2√3
√18 = 3√2
√20 = 2√5
√27 = 3√3
√28 = 2√7
√32 = 4√2
√44 = 2√11
√45 = 3√5
√48 = 4√3
√50 = 5√2
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Michelle
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Umm thanks, I guess.
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