Which expression is equivalent to sqrt 10 / 4 sqrt 8
Accepted Solution
A:
Answer:Step-by-step explanation:Keep in mind that we want to eliminate the radical from the denominator. Note that the denominator is equal to8^(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 2This result is the same as the first answer choice:fourth root of 200 over 2