SOLUTION: A very pleasant evening to you Math Solvers! I am encountering some difficulties about radicals, can you please help me. In my problems it is specified that you just need to simpli

Algebra ->  Radicals -> SOLUTION: A very pleasant evening to you Math Solvers! I am encountering some difficulties about radicals, can you please help me. In my problems it is specified that you just need to simpli      Log On


   

Question 120762: A very pleasant evening to you Math Solvers! I am encountering some difficulties about radicals, can you please help me. In my problems it is specified that you just need to simplify the following by reducing as much as possible, here it follows:
->fifth root of 486
Thank you very much!!!
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Start by trying to find all the factors of 486.
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Since 486 is an even number, obviously 2 is a factor. So you can write that:
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486+=+2%2A243
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Now try to factor 243. A little thought will convince you that 3 is a factor of 243. That
being the case, you can now say that:
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486+=+2%2A3%2A81
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Note that 81 can be factored into 9 times 9. So you now have:
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486+=+2%2A3%2A9%2A9
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But each of the 9's can be factored to 3*3 and this further reduces the problem to:
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486+=+2%2A3%2A3%2A3%2A3%2A3
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and since there are 5 factors of 3, you can further say:
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486+=+2%2A3%5E5
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The problem required you to find the 5th root of 486. You can substitute 2%2A3%5E5 for
486 and you have:
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root%285%2C486%29=+root%285%2C2%2A3%5E5%29+=+root%285%2C3%5E5%29%2Aroot%285%2C2%29
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But the 5th root of 3%5E5 is 3. Substituting this simplification reduces the problem to:
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root%285%2C486%29+=+3%2Aroot%285%2C2%29
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Hope this helps you to understand the problem.
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