Write the following expression in simplest form.

(Simplify your answer. Type an exact answer, using radicals as needed.)

Ask by Allan Sullivan. in the United States

Jan 24,2025

Question

Write the following expression in simplest form. $$ \sqrt{3^{2} \cdot 11^{4}} $$ $$ \sqrt{3^{2} \cdot 11^{4}}=\square $$ (Simplify your answer. Type an exact answer, using radicals as needed.)

UpStudy AI · Accepted Answer

To simplify the expression $$ \sqrt{3^{2} \cdot 11^{4}} $$, follow these steps:

1. **Break down the square root:**
   $$
   \sqrt{3^{2} \cdot 11^{4}} = \sqrt{3^{2}} \cdot \sqrt{11^{4}}
   $$

2. **Simplify each square root:**
   $$
   \sqrt{3^{2}} = 3
   $$
   $$
   \sqrt{11^{4}} = 11^{2} = 121
   $$

3. **Multiply the simplified terms:**
   $$
   3 \cdot 121 = 363
   $$

So, the simplest form of the expression is:

$$
\sqrt{3^{2} \cdot 11^{4}} = 363
$$

**Answer:**  
$$ 363 $$
$$ \sqrt{3^{2} \cdot 11^{4}} = 363 $$

Write the following expression in simplest form.

(Simplify your answer. Type an exact answer, using radicals as needed.)

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Write the following expression in simplest form. (Simplify your answer. Type an exact answer, using radicals as needed.)