Simplify seven square root of three end root minus four square root of six end root plus square root of forty eight end root minus square root of fifty four.

Question

a eleven square root of six end root minus seven square root of twelve
b eleven square root of three end root minus seven square root of six
c negative three square root of nine
d four square root of nine

Answer 1

Let's simplify the expression \( 7\sqrt{3} - 4\sqrt{6} + \sqrt{48} - \sqrt{54} \).

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

2. Simplifying \( \sqrt{54} \): \[ \sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \cdot \sqrt{6} = 3\sqrt{6} \]

3. Substituting back into the expression: \[ 7\sqrt{3} - 4\sqrt{6} + 4\sqrt{3} - 3\sqrt{6} \]

4. Combining like terms:

   • For \( \sqrt{3} \): \[ 7\sqrt{3} + 4\sqrt{3} = 11\sqrt{3} \]
   • For \( \sqrt{6} \): \[ -4\sqrt{6} - 3\sqrt{6} = -7\sqrt{6} \]

5. Final simplified expression: \[ 11\sqrt{3} - 7\sqrt{6} \]

Now, let's look at the answer choices:

a) \( 11\sqrt{6} - 7\sqrt{12} \)

b) \( 11\sqrt{3} - 7\sqrt{6} \)

c) \( -3\sqrt{9} \)

d) \( 4\sqrt{9} \)

The correct answer is b) \( 11\sqrt{3} - 7\sqrt{6} \).