What is the value of the expression `sqrt((m)/(x-3))` when `x = -1` and `m = -16`?

Options

A. `-2`
B. 2
C. `2sqrt(2)`
D. `2 i`

Answer

To find the value of the expression \(\sqrt{\frac{m}{x-3}}\) when \(x = -1\) and \(m = -16\), we can follow these steps:

### Step 1: Substitute the values of \(m\) and \(x\)
We start by substituting \(m = -16\) and \(x = -1\) into the expression:

\[ \sqrt{\frac{-16}{-1 - 3}} \]

### Step 2: Simplify the denominator
Next, we simplify the denominator:

\[ -1 - 3 = -4 \]

So, the expression now looks like:

\[ \sqrt{\frac{-16}{-4}} \]

### Step 3: Simplify the fraction
Now, we simplify the fraction \(\frac{-16}{-4}\):

\[ \frac{-16}{-4} = 4 \]

### Step 4: Take the square root
Now, we take the square root of 4:

\[ \sqrt{4} = 2 \]

### Final Answer
Thus, the value of the expression \(\sqrt{\frac{m}{x-3}}\) when \(x = -1\) and \(m = -16\) is:

\[ \boxed{2} \]

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