What is the simplified value of `sqrt18-1/sqrt2` ?

Options

A. `5//sqrt2`
B. `5sqrt2`
C. `2sqrt5`
D. `2//sqrt5`

Answer

To simplify the expression \( \sqrt{18} - \frac{1}{\sqrt{2}} \), we can follow these steps:

### Step 1: Simplify \( \sqrt{18} \)
We can break down \( \sqrt{18} \) as follows:
\[ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2} \]

### Step 2: Substitute \( \sqrt{18} \) back into the expression
Now we can rewrite the original expression:
\[ \sqrt{18} - \frac{1}{\sqrt{2}} = 3\sqrt{2} - \frac{1}{\sqrt{2}} \]

### Step 3: Find a common denominator
To combine the terms, we need a common denominator. The common denominator here is \( \sqrt{2} \):
\[ 3\sqrt{2} = \frac{3\sqrt{2} \cdot \sqrt{2}}{\sqrt{2}} = \frac{3 \cdot 2}{\sqrt{2}} = \frac{6}{\sqrt{2}} \]

### Step 4: Combine the fractions
Now we can combine the two fractions:
\[ \frac{6}{\sqrt{2}} - \frac{1}{\sqrt{2}} = \frac{6 - 1}{\sqrt{2}} = \frac{5}{\sqrt{2}} \]

### Step 5: Final expression
Thus, the simplified value of \( \sqrt{18} - \frac{1}{\sqrt{2}} \) is:
\[ \frac{5}{\sqrt{2}} \]