The fourth root of 24010000 is

Options

A. 7
B. 49
C. 490
D. 70

Answer

To find the fourth root of 24010000, we can follow these steps:

### Step 1: Rewrite the number
We can express the number 24010000 in a more manageable form. Notice that:
\[ 24010000 = 2401 \times 10000 \]

### Step 2: Break down the components
Next, we can find the fourth root of both components:
- The fourth root of \( 10000 \) is \( 10 \) because \( 10^4 = 10000 \).
- Now we need to find the fourth root of \( 2401 \).

### Step 3: Find the square root of 2401
To find the fourth root of \( 2401 \), we can first find the square root of \( 2401 \):
- We can pair the digits of \( 2401 \) as \( 24 \) and \( 01 \).
- The square root of \( 1 \) is \( 1 \).
- The square root of \( 24 \) can be estimated. The closest perfect squares are \( 16 \) (which is \( 4^2 \)) and \( 25 \) (which is \( 5^2 \)), so the square root of \( 24 \) is between \( 4 \) and \( 5 \).

### Step 4: Determine the exact square root
To find the exact square root of \( 2401 \):
- Testing \( 49 \) (which is \( 7^2 \)), we find that:
\[ 49 \times 49 = 2401 \]
Thus, \( \sqrt{2401} = 49 \).

### Step 5: Find the fourth root of 2401
Now, we can find the fourth root of \( 2401 \):
- Since \( \sqrt{2401} = 49 \), we take the square root of \( 49 \):
\[ \sqrt{49} = 7 \]

### Step 6: Combine the results
Now we can combine the results:
- The fourth root of \( 24010000 \) is:
\[ \sqrt[4]{24010000} = \sqrt[4]{2401} \times \sqrt[4]{10000} = 7 \times 10 = 70 \]

### Final Answer
Thus, the fourth root of \( 24010000 \) is \( 70 \).