Why does x / y = x / y / y Sorry for the awkward title, hard to to sum a mathematical problem with words alone.Having said that, I recently learned that the root of any value, x, and then that over value y, is identical to the root of x / y / y , as in x / y / y For e.g, 35 / 7 = 5 / 7 and I cannot logically deduce why. So far, I know that: 35 = 7 × 5 35 7 = 7 × 5 7 And somehow this being equal to:√(5/7)So it seems that we divided the numerator, √35 by √5 to give √7. However, 7/√7 is not √7! Yet, apparently it is?So, a fraction is of course equal to itself if scaled up or down by the same amount, in that 10/2 is the same as 5/1, or 5. So scaling down √35 by √5 makes sense, as it only leaves √7, but it seems that the same cannot be said for the denominator, 7. 7/√7 = √7!? Yet, the two expressions really are the same, √35/7 and √(5/7).Thanks for any help in advance.P.S This works for any values, so it's no coincidence.

Question

Why does       x        /    y  =      x          /        y          /        y  Sorry for the awkward title, hard to to sum a mathematical problem with words alone.Having said that, I recently learned that the root of any value, x, and then that over value y, is identical to the root of    x      /    y      /    y , as in       x          /        y          /        y  For e.g,       35        /    7  =      5          /        7    and I cannot logically deduce why. So far, I know that:  35  =  7  ×  5              35        7    =                    7            ×              5              7  And somehow this being equal to:√(5/7)So it seems that we divided the numerator, √35 by √5 to give √7. However, 7/√7 is not √7! Yet, apparently it is?So, a fraction is of course equal to itself if scaled up or down by the same amount, in that 10/2 is the same as 5/1, or 5. So scaling down √35 by √5 makes sense, as it only leaves √7, but it seems that the same cannot be said for the denominator, 7. 7/√7 = √7!? Yet, the two expressions really are the same, √35/7 and √(5/7).Thanks for any help in advance.P.S This works for any values, so it&#039;s no coincidence.

Jake Mcpherson · Accepted Answer

The typesetting is difficult to understand, perhaps this is what you&#039;re looking far :                                                        b                                      x            y        =                                                        b                                      x                              y          2                      =                                                                        b                                              x                          y          2                      .So for your example with x=35 and y=7 we get :                    35            7        =                              35                          7          2                      =                              7          ⋅          5                          7          ⋅          7                      =                    5        7              .

Sonia Gay · Accepted Answer

I expect you are aware that            a      ⋅      b        b    =  abecause we can cancel the b in the numerator and denominator.The piece you seem to be missing is that      a          a        =                    a                    a                    a        =      a  where in the last step we canceled       a   from the numerator and denominator.Or put another way, you know that if   x  y  =  z then   x  =      z    y  . Take   x  =      a    ,  y  =      a    ,  z  =  a . Then      a        a    =  a  ,so dividing by       a   on both sides we get       a    =      a          a

Why does <msqrt> x </msqrt> <mrow class="MJX-TeXAtom-ORD"> / </mrow> y = <msq

Answered question

Answer & Explanation

New Questions in Pre-Algebra