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Thread: Fractions (Adv)

  1. #1
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    Fractions (Adv)



    Taken from another post. How would you evaluate that fraction, or specifically (out of my homework) 4rt(81) [note that the 4 is the n). I got the bright idea that it might be rooted 4 times, but I get rt(3) and my math book says it's simply 3. Please explain.

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by Harness View Post


    Taken from another post. How would you evaluate that fraction, or specifically (out of my homework) 4rt(81) [note that the 4 is the n). I got the bright idea that it might be rooted 4 times, but I get rt(3) and my math book says it's simply 3. Please explain.

    Thanks in advance.
    Observe that $\displaystyle x = 81^{1/4} = (81^{1/2})^{1/2} = 9^{1/2} = 3$

    So to find $\displaystyle x$, square root 81 twice, once to get 9 and a second time to get the answer: 3.

    Raising a number to the one-fourth power does not mean that you are square rooting it four times. Instead, it is asking: which number multiplied by itself four times gets you the original number? In other words, which number multiplied by itself four times gets you 81? That number is defined as $\displaystyle 81^{1/4}$, or 3.
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  3. #3
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    Quote Originally Posted by Last_Singularity View Post
    Observe that $\displaystyle x = 81^{1/4} = (81^{1/2})^{1/2} = 9^{1/2} = 3$

    So to find $\displaystyle x$, square root 81 twice, once to get 9 and a second time to get the answer: 3.

    Raising a number to the one-fourth power does not mean that you are square rooting it four times. Instead, it is asking: which number multiplied by itself four times gets you the original number? In other words, which number multiplied by itself four times gets you 81? That number is defined as $\displaystyle 81^{1/4}$, or 3.
    Okay, thanks, that makes sense to me
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