2. $$ \sqrt{48}-\sqrt{12}+\sqrt{27} $$

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UpStudy AI · Accepted Answer

To simplify the expression $$ \sqrt{48} - \sqrt{12} + \sqrt{27} $$, follow these steps:

1. **Factor Each Square Root:**

Break down each term into its prime factors to identify perfect squares.

- $$ \sqrt{48} $$:
     $$
     48 = 16 \times 3 = 4^2 \times 3
     $$
     $$
     \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
     $$

- $$ \sqrt{12} $$:
     $$
     12 = 4 \times 3 = 2^2 \times 3
     $$
     $$
     \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
     $$

- $$ \sqrt{27} $$:
     $$
     27 = 9 \times 3 = 3^2 \times 3
     $$
     $$
     \sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}
     $$

2. **Substitute the Simplified Terms Back into the Expression:**

$$
   \sqrt{48} - \sqrt{12} + \sqrt{27} = 4\sqrt{3} - 2\sqrt{3} + 3\sqrt{3}
   $$

3. **Combine Like Terms:**

Since all terms have the common factor $$ \sqrt{3} $$, you can combine the coefficients:

$$
   4\sqrt{3} - 2\sqrt{3} + 3\sqrt{3} = (4 - 2 + 3)\sqrt{3} = 5\sqrt{3}
   $$

**Final Simplified Form:**

$$
5\sqrt{3}
$$
$$ 5\sqrt{3} $$

2. \( \sqrt{48}-\sqrt{12}+\sqrt{27} \)

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