Square root fraction confusionI was doing math for school and got to something that really confused me. With having the rule 2 4 = 4 8 (or some simular fraction equation) in mind, I got to the following confusing equation: 3 3 = ( 3 ) 2 3 2 = 3 9 = 1 3 This is really confusing me since 3 3 can never equal 1 3 . Where am I going wrong?

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Square root fraction confusionI was doing math for school and got to something that really confused me. With having the rule       2    4    =      4    8   (or some simular fraction equation) in mind, I got to the following confusing equation:            3        3    =            (              3                    )        2                    3      2        =      3    9    =      1    3  This is really confusing me since             3        3   can never equal       1    3  . Where am I going wrong?

Carmelo Payne · Accepted Answer

It is incorrect that             3        3    =                    3            2              3      2      . A simple way of seeing this is because you can multiply both the top and the bottom of a fraction by the same number, but in this case, you are multiplying       3   to the top, and   3 to the bottom, but       3    ≠  3, so they are different numbers. What you proved, instead, is that             (                  3        3                      )              2    =      1    3  , which is true.

Petrovcic2x · Accepted Answer

In general             a      b        ≠                    a        2                    b        2            . You can multiply both the numerator and the denominator by the same number, but not by different numbers.

Square root fraction confusion I was doing math for school and got to something that really confuse

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