Question

lindsey simplified the radical expression \\(\sqrt{50}\\) as shown.

step 1: \\(\sqrt{5 \cdot 5 \cdot 2}\\)
step 2: \\(\sqrt{5^2} \cdot \sqrt{2}\\)
step 3: \\(5\sqrt{2}\\)

did lindsey make a mistake?

• yes, in step 1 she should have written \\(\sqrt{2 \cdot 2 \cdot 5}\\). her final answer should have been \\(2\sqrt{5}\\).
• yes, in step 3 she should have found a final answer of 10.
• no, all of her work is correct.
• yes, in step 2 she should have written \\(\sqrt{5^2 \cdot 2}\\).

Explanation:

Step 1: Analyze Step 1

$$\sqrt{50} = \sqrt{5 \cdot 5 \cdot 2}$$

Since \(5 \cdot 5 \cdot 2 = 50\), this step is correct.

Step 2: Analyze Step 2

$$\sqrt{5 \cdot 5 \cdot 2} = \sqrt{5^2} \cdot \sqrt{2}$$

Using the product property of radicals, this step is correct.

Step 3: Analyze Step 3

$$\sqrt{5^2} \cdot \sqrt{2} = 5\sqrt{2}$$

Since \(\sqrt{5^2} = 5\), the simplification is correct.

Answer:

No, all of her work is correct.