Your answer is incorrect. Simplify. $$ \sqrt{12 t^{9} w^{8}} $$ Assume that all variables represent positive rea

Question

UpStudy AI · Accepted Answer

We start with the expression

$$
\sqrt{12t^9w^8}.
$$

**Step 1. Factor the radicand into perfect squares:**

$$
12t^9w^8 = 4 \cdot 3 \cdot (t^8 \cdot t) \cdot w^8.
$$

**Step 2. Rewrite the square root using the factorization:**

$$
\sqrt{12t^9w^8} = \sqrt{4t^8w^8 \cdot 3t}.
$$

**Step 3. Separate the square root into two parts:**

$$
\sqrt{4t^8w^8 \cdot 3t} = \sqrt{4t^8w^8} \cdot \sqrt{3t}.
$$

**Step 4. Simplify the first square root by taking the square root of each perfect square:**

$$
\sqrt{4} = 2, \quad \sqrt{t^8} = t^4, \quad \sqrt{w^8} = w^4.
$$

Thus,

$$
\sqrt{4t^8w^8} = 2t^4w^4.
$$

**Step 5. Combine the results:**

$$
\sqrt{12t^9w^8} = 2t^4w^4 \sqrt{3t}.
$$
$$ \sqrt{12t^9w^8} = 2t^4w^4 \sqrt{3t} $$

Your answer is incorrect.
Simplify.

Assume that all variables represent positive rea