Question

Evaluate the square root of 0.000562 using logarithm table?

Answer 1

To evaluate the square root of \( 0.000562 \) using logarithmic tables, we can follow these steps:

1. **Convert to Scientific Notation**:
\[
0.000562 = 5.62 \times 10^{-4}
\]

2. **Logarithm of the Number**:
Next, we find the logarithm of \( 5.62 \). If we can access a logarithm table, we look up \( \log_{10}(5.62) \).

From standard logarithm tables or calculators:
\[
\log_{10}(5.62) \approx 0.75
\]

3. **Adding Logarithm of the Power of Ten**:
Since we have \( 5.62 \times 10^{-4} \):
\[
\log_{10}(0.000562) = \log_{10}(5.62) + \log_{10}(10^{-4}) \\
= \log_{10}(5.62) - 4
\]
Substituting the value we found:
\[
\log_{10}(0.000562) \approx 0.75 - 4 = -3.25
\]

4. **Finding the Square Root**:
The square root can be found by halving the logarithm:
\[
\log_{10}(\sqrt{0.000562}) = \frac{1}{2} \log_{10}(0.000562) \\
= \frac{1}{2} \cdot (-3.25) = -1.625
\]

5. **Finding the antilogarithm**:
Now we need to find \( 10^{-1.625} \). This may also require a logarithm table, or we can calculate it as:
\[
10^{-1.625} \approx 0.0234
\]

Thus, the square root of \( 0.000562 \) is approximately:
\[
\sqrt{0.000562} \approx 0.0234
\]