Question

choose three correct answers of the following that are like radicals.
$9\sqrt{6ab^2}$ $2\sqrt{6b^2a}$ $-5\sqrt{6ab^2}$ $4\sqrt3{6ab^2}$

Explanation:

Step1: Recall like radicals definition

Like radicals have same radicand (expression under root) and same index (root type, e.g., square root has index 2, cube root index 3).

Step2: Analyze each radical

• For \( 9\sqrt{6ab^2} \): Radicand is \( 6ab^2 \), index 2 (square root).
• For \( 2\sqrt{6b^2a} \): Simplify radicand \( 6b^2a = 6ab^2 \) (multiplication commutative), index 2. So radicand same as first, index same.
• For \( -5\sqrt{6ab^2} \): Radicand \( 6ab^2 \), index 2. Same as first two.
• For \( 4\sqrt[3]{6ab^2} \): Index 3 (cube root), different from others (index 2). So not like.

Step3: Identify like radicals

\( 9\sqrt{6ab^2} \), \( 2\sqrt{6b^2a} \), \( -5\sqrt{6ab^2} \) have same radicand (\( 6ab^2 \)) and same index (2).

Answer:

\( 9\sqrt{6ab^2} \), \( 2\sqrt{6b^2a} \), \( -5\sqrt{6ab^2} \)