Which expression is equivalent to sqrt 10 / 4 sqrt 8

Step-by-step explanation:

Keep in mind that we want to eliminate the radical from the denominator.  Note that the denominator is equal to

8^(1/4) = (2^3)^(1/4).

If we multiply the entire given expression by 2^(1/4), we get:

2^(1/4)           √10

*

2^(1/4)       (2^3)^(1/4)

or

2^(1/4)           √10            2^(1/4) · √10          2^(1/4) · 10^(2/4)    

* = =

2^(1/4)       (2^3)^(1/4)         2^(1/4 + 3/4)                2                          

    2^(1/4) · 10^(2/4)           2^(1/4) · 100^(1/4)        200^(1/4)

= = =

                 2                                   2                           2

This result is the same as the first answer choice:

fourth root of 200   over   2

2

the first one, all those points on the line just make a strait line.