Simplify the radical expression. $$ \sqrt{50} $$

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UpStudy AI · Accepted Answer

To simplify the radical expression $$\sqrt{50}$$, follow these steps:

1. **Factor the Number Inside the Radical:**
   
   Break down 50 into its prime factors:
   $$
   50 = 25 \times 2
   $$
   Here, 25 is a perfect square since $$25 = 5^2$$.

2. **Apply the Square Root Property:**
   
   The square root of a product is the product of the square roots:
   $$
   \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2}
   $$

3. **Simplify the Square Root:**
   
   Since $$\sqrt{25} = 5$$, substitute this value:
   $$
   \sqrt{50} = 5 \times \sqrt{2} = 5\sqrt{2}
   $$

**Final Simplified Form:**
$$
\sqrt{50} = 5\sqrt{2}
$$
$$ \sqrt{50} = 5\sqrt{2} $$

Simplify the radical expression.

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