Combine the radicals using addition and subtraction if possible five radical 48 - 6 radical 3 + 2 radical 12

Answer 1

To combine the radicals \(5 \sqrt{48} - 6 \sqrt{3} + 2 \sqrt{12}\), we first simplify each radical.

Step 1: Simplify \( \sqrt{48} \) and \( \sqrt{12} \)

1. For \( \sqrt{48} \): \[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \cdot \sqrt{3} = 4\sqrt{3} \]

2. For \( \sqrt{12} \): \[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \]

Step 2: Substitute back into the original expression

Now we can substitute these simplifications back into the original expression:

\[ 5\sqrt{48} - 6\sqrt{3} + 2\sqrt{12} \] becomes \[ 5(4\sqrt{3}) - 6\sqrt{3} + 2(2\sqrt{3}) \]

Step 3: Compute the coefficients

Now we can compute: \[ = 20\sqrt{3} - 6\sqrt{3} + 4\sqrt{3} \]

Step 4: Combine like terms

Now we combine the coefficients of \( \sqrt{3} \): \[ (20 - 6 + 4)\sqrt{3} = 18\sqrt{3} \]

Thus, the final result is: \[ \boxed{18\sqrt{3}} \]