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sqrt[4]{6} times sqrt[4]{36} times sqrt[4]{192}

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lol, more of a fail -.- So, this is the question: \[\sqrt[4]{6} \times \sqrt[4]{36} \times \sqrt[4]{192}\]
I know it looks easy, I just keep on getting different answer :/

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Other answers:

I got \[2\sqrt[4]{2592}\] Yeah -.- It looks wrong -.-
If it has the same root....
rewrite it like this: \[\large \sqrt[4]{6 \times 36 \times 192}\]
Yes, this is what I did..
  • phi
I would never multiply these numbers together. on the contrary, you want to factor them all are under the root sign. so you have \[ 6 \cdot 6^2 \cdot 6\cdot 2^5 \] or \[ 6^4 \cdot 2^4 \cdot 2\] pull out the powers of 4
I didn't multiply them together. I just simplified them under one root @phi. I agree that what you did would be the next step AFTER putting them under one root
sorry. i got \[ \large 12\sqrt[4]{2} \]
  • phi
@Hero that was to @aroub not you. I know you know how to do it!
I didn't multiply them together at first. This is was what I did (it's stupid though compared to what you did): \[\sqrt[4]{3\times2 \times 6^2\times2^6\times3} = \sqrt[4]{3^2\times2^4\times6^2\times2^3}\] Don't ask me how or why :P And then after realizing I cant factor them more I multiplied them.
Thank you phi and everyone!! =D
  • phi
doing that is fine. The only mistake is not factor the 6^2 into 2^2 * 3^2 after combining bases, you would have gotten 3^4 2^9 or 3^4 * 2^4 * 2^4 * 2 take the 4th root, you would get 3*2*2 * 2^(1/4) or 12* 2^(1/4)
If i still want the square root that would be equal to \[12\sqrt[4]{2}?\]
  • phi
yes, but it is the 4th root (not the square root)
Oh yeah sorry -.- I'm used to square roots :P

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