Is 7 15 3 rational or irrational? Prove it. I am having a hard time with this question. So far what I did was say, assume it's rational, then 7 15 3 = x y ⇒ 7 y = x 15 3 I then showed the product of a rational number and an irrational number is irrational so the expression above is irrational on the left and right side. I can't get to a contradiction to prove it's irrational so I'm currently thinking it is rational but I don't know how to go about proving it.

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Is             7              15      3       rational or irrational? Prove it. I am having a hard time with this question. So far what I did was say, assume it&#039;s rational, then            7              15      3        =      x    y    ⇒      7    y  =  x      15    3  I then showed the product of a rational number and an irrational number is irrational so the expression above is irrational on the left and right side. I can&#039;t get to a contradiction to prove it&#039;s irrational so I&#039;m currently thinking it is rational but I don&#039;t know how to go about proving it.

bshizzey7h · Accepted Answer

Suppose the number is rational, let            7              15      3        =      x    y  where   gcd  (  x  ,  y  )  =  1, then      7    y  =      15    3    x    ⟹        7    3        y    6    =  225      x    6  So      7    3        |        x    6  which implies   7      |    xLet   x  =  7  m  ,    m  ∈      N  . Then we have      7    3        y    6    =  225  ×      7    6        m    6  which means      y    6    =  225  ×      7    3        m    6  once again we have      7    3        |        y    6  which implies   7      |    y. And this is contradictory to the coprimality between x and y.

katkoota00ys · Accepted Answer

Factoring          7                                  3                          y                  6                =      15                  2                  x                            6                     into primes,     7   has odd power     3    +    6  j   on LHS, but even     6  k   on RHS

Is <msqrt> 7 </msqrt> <mroot> 15 3 </mroot> </mfrac

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