`3sqrt(21952)+33=?`

Options

A. 58
B. 61
C. 63
D. 51

Explanation

To solve the equation \(3\sqrt{21952} + 33 = ?\), we will follow these steps:

### Step 1: Identify the cube root
We need to find the cube root of \(21952\). We can express \(21952\) in terms of its prime factors or check if it is a perfect cube.

### Step 2: Factor \(21952\)
We can find the prime factorization of \(21952\):
- Divide \(21952\) by \(2\):
- \(21952 \div 2 = 10976\)
- \(10976 \div 2 = 5488\)
- \(5488 \div 2 = 2744\)
- \(2744 \div 2 = 1372\)
- \(1372 \div 2 = 686\)
- \(686 \div 2 = 343\)
- Now, \(343\) is \(7^3\) (since \(7 \times 7 \times 7 = 343\)).

So, we can express \(21952\) as:
\[ 21952 = 2^6 \times 7^3 \]

### Step 3: Calculate the cube root
Now, we can find the cube root:
\[ \sqrt[3]{21952} = \sqrt[3]{2^6 \times 7^3} = \sqrt[3]{(2^2)^3 \times 7^3} = 2^2 \times 7 = 4 \times 7 = 28 \]

### Step 4: Substitute back into the equation
Now we substitute back into the original equation:
\[ 3\sqrt[3]{21952} + 33 = 3 \times 28 + 33 \]

### Step 5: Perform the multiplication
Calculate \(3 \times 28\):
\[ 3 \times 28 = 84 \]

### Step 6: Add \(33\)
Now, add \(33\) to \(84\):
\[ 84 + 33 = 117 \]

### Final Answer
Thus, the final answer is:
\[ ? = 117 \]

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