Simplify $$ 3 \sqrt{450}-\sqrt{32} $$ $$ [?] \sqrt{[\square}] $$

Question

UpStudy AI · Accepted Answer

Let's simplify the expression step by step:

$$ 3 \sqrt{450} - \sqrt{32} $$

1. **Simplify $$\sqrt{450}$$:**

$$
   450 = 225 \times 2 = 15^2 \times 2
   $$
   
   $$
   \sqrt{450} = \sqrt{15^2 \times 2} = 15\sqrt{2}
   $$
   
   Therefore,

$$
   3\sqrt{450} = 3 \times 15\sqrt{2} = 45\sqrt{2}
   $$

2. **Simplify $$\sqrt{32}$$:**

$$
   32 = 16 \times 2 = 4^2 \times 2
   $$
   
   $$
   \sqrt{32} = \sqrt{4^2 \times 2} = 4\sqrt{2}
   $$

3. **Combine the simplified terms:**

$$
   3\sqrt{450} - \sqrt{32} = 45\sqrt{2} - 4\sqrt{2} = (45 - 4)\sqrt{2} = 41\sqrt{2}
   $$

**Final Simplified Form:**

$$
41 \sqrt{2}
$$

Answer: $$41 \sqrt{2}$$
$$41 \sqrt{2}$$

Simplify \( 3 \sqrt{450}-\sqrt{32} \) \( [?] \sqrt{[\square}] \)