Find the value of question mark(?) in the following questions ?
`root(3)(29791)`=?

Options

A. 33
B. 31
C. 27
D. 37

Answer

To find the value of \( \sqrt[3]{29791} \), we will follow these steps:

### Step 1: Identify the cube root
We need to find the cube root of 29791, which means we are looking for a number \( x \) such that \( x^3 = 29791 \).

### Step 2: Factor 29791
We can start by checking if 29791 can be factored into smaller components. We will check for divisibility by small prime numbers.

### Step 3: Check divisibility by 31
After testing various small prime numbers, we find that 29791 is divisible by 31. Let's divide:
\[ 29791 \div 31 = 961 \]

### Step 4: Factor 961
Now, we need to check if 961 can be factored further. We can check if 961 is a perfect square:
\[ 31 \times 31 = 961 \]
Thus, we can express 961 as:
\[ 961 = 31^2 \]

### Step 5: Combine the factors
Now we can express 29791 as:
\[ 29791 = 31 \times 961 = 31 \times (31 \times 31) = 31^3 \]

### Step 6: Calculate the cube root
Now that we have expressed 29791 as \( 31^3 \), we can find the cube root:
\[ \sqrt[3]{29791} = \sqrt[3]{31^3} = 31 \]

### Final Answer
Thus, the value of \( \sqrt[3]{29791} \) is \( 31 \).

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