Find x, if :
`sqrt(2^(x+3)) = 16`

Answer

To solve the equation \( \sqrt{2^{(x+3)}} = 16 \), we can follow these steps:

### Step 1: Rewrite the square root in exponent form
The square root can be expressed as an exponent of \( \frac{1}{2} \):
\[ \sqrt{2^{(x+3)}} = 2^{(x+3)/2} \]

### Step 2: Rewrite 16 as a power of 2
Next, we rewrite 16 as a power of 2:
\[ 16 = 2^4 \]

### Step 3: Set the exponents equal to each other
Since we have \( 2^{(x+3)/2} = 2^4 \), we can set the exponents equal to each other:
\[ \frac{x+3}{2} = 4 \]

### Step 4: Solve for \( x \)
To eliminate the fraction, multiply both sides by 2:
\[ x + 3 = 8 \]
Now, subtract 3 from both sides:
\[ x = 8 - 3 \]
\[ x = 5 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{5} \]

---