Answer:
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
