The value of `sqrt(2^(4))+root(3)(64)+root(4)(2^(8))` is :

Options

A. `12`
B. `16`
C. `18`
D. `24`

Answer

To solve the expression \( \sqrt{2^4} + \sqrt[3]{64} + \sqrt[4]{2^8} \), we will simplify each term step by step.

### Step 1: Simplify \( \sqrt{2^4} \)
The square root of \( 2^4 \) can be simplified as follows:
\[ \sqrt{2^4} = 2^{4/2} = 2^2 = 4 \]

### Step 2: Simplify \( \sqrt[3]{64} \)
Next, we simplify the cube root of 64. We know that:
\[ 64 = 4^3 = (2^2)^3 = 2^6 \]
Thus, we can write:
\[ \sqrt[3]{64} = \sqrt[3]{2^6} = 2^{6/3} = 2^2 = 4 \]

### Step 3: Simplify \( \sqrt[4]{2^8} \)
Now, we simplify the fourth root of \( 2^8 \):
\[ \sqrt[4]{2^8} = 2^{8/4} = 2^2 = 4 \]

### Step 4: Combine all the simplified terms
Now we can combine all the simplified terms:
\[ \sqrt{2^4} + \sqrt[3]{64} + \sqrt[4]{2^8} = 4 + 4 + 4 = 12 \]

### Final Answer
The value of the expression \( \sqrt{2^4} + \sqrt[3]{64} + \sqrt[4]{2^8} \) is \( 12 \).

---