`(sqrt(8)-sqrt(4)-sqrt(2))` equals :

Options

A. a) `2-sqrt(2)`
B. b) `sqrt(2)-2`
C. c) `2`
D. d) `-2`

Answer

To solve the expression \( \sqrt{8} - \sqrt{4} - \sqrt{2} \), we will simplify each square root step by step.

### Step 1: Simplify each square root
- \( \sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \)
- \( \sqrt{4} = 2 \)
- \( \sqrt{2} \) remains as \( \sqrt{2} \)

### Step 2: Substitute the simplified values back into the expression
Now we can substitute the simplified square roots back into the expression:
\[ \sqrt{8} - \sqrt{4} - \sqrt{2} = 2\sqrt{2} - 2 - \sqrt{2} \]

### Step 3: Combine like terms
Next, we will combine the terms involving \( \sqrt{2} \):
\[ 2\sqrt{2} - \sqrt{2} = (2 - 1)\sqrt{2} = 1\sqrt{2} = \sqrt{2} \]
So, the expression now becomes:
\[ \sqrt{2} - 2 \]

### Final Answer
Thus, the value of the expression \( \sqrt{8} - \sqrt{4} - \sqrt{2} \) is:
\[ \sqrt{2} - 2 \]

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