Question

3When 1,250^3/4 is written in its simplest radical form, which value remains under the radical?O 10O 6O 502

Answer 1

The given expression is:

$1250^{\frac{3}{4}}$

Find the prime factorization of the number 1250:

$1250=2\times5^4$

Therefore,

$\begin{gathered} 1250^{\frac{3}{4}}=(2\times5^4)^{\frac{3}{4}}=5^{4\times\frac{3}{4}}\times2^{\frac{3}{4}} \\ =5^3\times2^{\frac{3}{4}} \\ =125(\sqrt[4]{2})^3 \end{gathered}$

Therefore, the number that remains under the radical is 2.

Hence, the correct answer is 2