How to simplify 3 / 2 My textbook says to do the following steps to simplify the 3 / 2 3 / 2 = ( ( 3 / 2 ) × ( 2 / 2 ) ) = 6 / 4 = 6 / 4 = 6 / 2.However, if the fourth step is valid (1. please explain why and 2. I specifically mean where you "split" the square root into two parts), then why can't you simply do: 3 / 2 = 3 / 2 3 / 2 = 3 / 2 Why wouldn't that be valid?My point is, are the two fractions equivalent?

Question

How to simplify       3          /        2  My textbook says to do the following steps to simplify the       3          /        2        3          /        2    =      (    (    3          /        2    )    ×    (    2          /        2    )    )    =      6          /        4    =      6        /        4    =      6        /    2.However, if the fourth step is valid (1. please explain why and 2. I specifically mean where you &quot;split&quot; the square root into two parts), then why can&#039;t you simply do:      3          /        2    =      3        /        2        3          /        2    =      3        /        2  Why wouldn&#039;t that be valid?My point is, are the two fractions equivalent?

Erika Ayers · Accepted Answer

It is true that            3      2        =            3              2        .Generally, when one simplifies fractions involving square roots, you want to remove all square roots in the demoninator so            3      2        =            3              2        =            3              2        ⋅            2              2        =                    3                    2              2  You also have that            6        2    =            3      ⋅      2        2    =                    3                    2              2    ,so you can write the same things in different ways:            3      2        =            3              2        =            6        2    =                    3                    2              2    .It just depends on what is considered &quot;most simplified.&quot;

Direkotogbkmn · Accepted Answer

It is true that       3          /        2   is equal to       3        /        2  However, the point of the transformations you give it to have a denominator without root.More generally, for positive   a  ,  b it is always true that       a    b    =      a        b   and       a          /        b    =      a        /        b  To see that note   (      a        b        )    2    =  (      a        )    2    (      b        )    2    =  a  b, thus       a        b   is the square-root of   a  b, that is it is       a    b  . And likewise for the second.

How to simplify <msqrt> 3 <mrow class="MJX-TeXAtom-ORD"> / </mrow> 2

Answered question

Answer & Explanation

New Questions in Pre-Algebra