Santiago Powers
10/03/2023 · Primary School
\( 51^{2}\div 316\sqrt {25_{45}}=2x \)
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Tutor-Verified Answer
Step-by-step Solution
To solve the equation \( 51^{2} \div 316\sqrt {25_{45}} = 2x \), we will break it down step by step.
1. **Calculate \( 51^2 \)**:
\[
51^2 = 2601
\]
2. **Convert \( 25_{45} \) to decimal**:
The notation \( 25_{45} \) means that 25 is in base 45. To convert it to decimal:
\[
25_{45} = 2 \cdot 45^1 + 5 \cdot 45^0 = 2 \cdot 45 + 5 \cdot 1 = 90 + 5 = 95
\]
3. **Calculate \( \sqrt{25_{45}} \)**:
\[
\sqrt{25_{45}} = \sqrt{95}
\]
4. **Substitute back into the equation**:
Now we substitute \( 51^2 \) and \( \sqrt{25_{45}} \) back into the equation:
\[
2601 \div (316 \cdot \sqrt{95}) = 2x
\]
5. **Calculate \( 316 \cdot \sqrt{95} \)**:
We will leave \( \sqrt{95} \) as is for now. Thus, we have:
\[
2601 \div (316 \cdot \sqrt{95}) = 2x
\]
6. **Calculate \( 2601 \div 316 \)**:
\[
2601 \div 316 \approx 8.23 \quad (\text{using a calculator})
\]
7. **Now we have**:
\[
\frac{8.23}{\sqrt{95}} = 2x
\]
8. **Solve for \( x \)**:
\[
x = \frac{8.23}{2\sqrt{95}}
\]
9. **Calculate \( \sqrt{95} \)**:
\[
\sqrt{95} \approx 9.74679
\]
10. **Now substitute \( \sqrt{95} \) back into the equation**:
\[
x \approx \frac{8.23}{2 \cdot 9.74679} \approx \frac{8.23}{19.49358} \approx 0.422
\]
Thus, the value of \( x \) is approximately \( 0.422 \).
Quick Answer
The value of \( x \) is approximately \( 0.422 \).
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