`3sqrt(42875)-?=21`

Options

A. 18
B. 13
C. 15
D. None of these

Explanation

To solve the equation \( 3\sqrt{42875} - ? = 21 \), we will follow these steps:

1. **Identify the expression**: We need to isolate the question mark \( ? \) in the equation. The equation can be rewritten as:
\[ 3\sqrt{42875} - ? = 21 \]

2. **Isolate the question mark**: We can rearrange the equation to solve for \( ? \):
\[ ? = 3\sqrt{42875} - 21 \]

3. **Calculate \( \sqrt{42875} \)**: Next, we need to find the value of \( \sqrt{42875} \). We can simplify \( 42875 \) by factoring it:
- First, we can divide \( 42875 \) by \( 25 \) (since it ends in 75):
\[ 42875 \div 25 = 1715 \]
- Next, we can divide \( 1715 \) by \( 5 \):
\[ 1715 \div 5 = 343 \]
- Now, we can factor \( 343 \) as \( 7^3 \):
\[ 343 = 7 \times 7 \times 7 \]
- Therefore, we can express \( 42875 \) as:
\[ 42875 = 25 \times 5 \times 343 = 25 \times 5 \times 7^3 \]

4. **Calculate \( \sqrt{42875} \)**: Now we can find \( \sqrt{42875} \):
\[ \sqrt{42875} = \sqrt{25 \times 5 \times 343} = \sqrt{25} \times \sqrt{5} \times \sqrt{343} = 5 \times \sqrt{5} \times 7 = 35\sqrt{5} \]

5. **Substitute back into the equation**: Now we substitute \( \sqrt{42875} \) back into the equation:
\[ ? = 3(35\sqrt{5}) - 21 \]
\[ ? = 105\sqrt{5} - 21 \]

6. **Final calculation**: The value of \( ? \) is:
\[ ? = 105\sqrt{5} - 21 \]

Thus, the value of \( ? \) is \( 105\sqrt{5} - 21 \).