Solution 3.1:3b

From Förberedande kurs i matematik 1

When simplifying a radical expression, a common technique is to divide up the numbers under the root sign into their smallest possible integer factors and then take out the squares and see if common factors cancel each other out or can be combined together in a new way.

By successively dividing by 2 and 3, we see that

9618=248=2224=22212=22226=222223=253=29=233=232

Thus,

9618=253=222223=2223=232=32

and the whole quotient can be written as

1896=322223=343.

Note: If it is difficult to work with radicals, it is possible instead to write everything in power form

1896=18129612=(232)12(253)12=22132212521321=225−21321−1=223−21=43=343.

(In the last equality, we multiply top and bottom by 3 .)