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: Express the number in a suitable form
We start with the number 24010000. We can express this number in terms of its prime factors or in a way that makes it easier to find the fourth root.

### Step 2: Factor the number
We can break down 24010000 into smaller components. Notice that:
\[ 24010000 = 2401 \times 10000 \]

### Step 3: Factor each component
Next, we can factor 2401 and 10000:
- \( 2401 = 7^4 \) (since \( 7 \times 7 \times 7 \times 7 = 2401 \))
- \( 10000 = 10^4 \) (since \( 10 \times 10 \times 10 \times 10 = 10000 \))

### Step 4: Rewrite the original number
Now we can rewrite 24010000 using these factors:
\[ 24010000 = 7^4 \times 10^4 \]

### Step 5: Apply the fourth root
Now, we can find the fourth root of the entire expression:
\[ \sqrt[4]{24010000} = \sqrt[4]{7^4 \times 10^4} \]

Using the property of roots, we can separate the terms:
\[ \sqrt[4]{7^4} \times \sqrt[4]{10^4} \]

### Step 6: Simplify the expression
Now we can simplify each term:
- \( \sqrt[4]{7^4} = 7 \)
- \( \sqrt[4]{10^4} = 10 \)

So we have:
\[ \sqrt[4]{24010000} = 7 \times 10 = 70 \]

### Conclusion
Thus, the fourth root of 24010000 is:
\[ \boxed{70} \]

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