Question

select all of the following that are like radicals. 9\sqrt{6ab^{2}} -5\sqrt{6ab^{2}} 4\sqrt3{6ab^{2}} 2\sqrt{6b^{2}a}

Explanation:

Step1: Define like radicals

Like radicals have the same index (root degree) and same radicand (expression under the root).

Step2: Analyze each option

1. $9\sqrt{6ab^2}$: Index = 2, Radicand = $6ab^2$
2. $-5\sqrt{6ab^2}$: Index = 2, Radicand = $6ab^2$
3. $4\sqrt[3]{6ab^2}$: Index = 3, Radicand = $6ab^2$
4. $2\sqrt{6b^2a}$: Index = 2, Radicand = $6ab^2$ (since multiplication is commutative, $6b^2a=6ab^2$)

Step3: Match like radicals

Options 1, 2, 4 share index 2 and identical radicand $6ab^2$. Option 3 has a different index (3), so it is not a like radical.

Answer:

• $9\sqrt{6ab^2}$
• $-5\sqrt{6ab^2}$
• $2\sqrt{6b^2a}$