Question

simplify the radical expression, if possible.
$3\sqrt{7} - 5\sqrt3{7}$
options: $-2\sqrt{7}$, $-2\sqrt3{7}$, cannot be simplified

Explanation:

Step1: Check radical indices

The first term is \(3\sqrt{7}\) (square root, index 2) and the second is \(5\sqrt[3]{7}\) (cube root, index 3).

Step2: Determine simplifiability

Radical terms can only be combined if they have the same index and radicand. Here, indices (2 vs 3) differ, so they can't be combined.

Answer:

cannot be simplified