PREVIOUSLY ASKED IN:
WBPSC Miscellaneous Preliminary 2023
Answer
0.008
Explanation
A quick rule for finding the square root of a decimal number is to count the decimal places. The square root will have exactly half the number of decimal places as the original number. In \( 0.000064 \), there are 6 decimal places. The square root of 64 is 8. Therefore, the answer must have 3 decimal places, making it \( 0.008 \). Verification: \( 0.008 \times 0.008 = 0.000064 \).
Key Points
- > Square root of whole number: \( \sqrt{64} = 8 \).
- > 6 decimal places inside root \( \rightarrow \) 3 decimal places outside.
- > Fraction method: \( \sqrt{\frac{64}{1000000}} = \frac{8}{1000} = 0.008 \).
- > If it was \( \sqrt{0.0064} \), the answer would be 0.08 (half of 4 places).
- > If it was \( \sqrt{0.64} \), the answer would be 0.8 (half of 2 places).
Additional Information
Decimal Square Root Patterns
| Problem | Decimal Places (In) | Answer | Decimal Places (Out) |
|---|---|---|---|
| \( \sqrt{0.25} \) | 2 | \( 0.5 \) | 1 |
| \( \sqrt{0.0025} \) | 4 | \( 0.05 \) | 2 |
| \( \sqrt{0.000025} \) | 6 | \( 0.005 \) | 3 |
Memory Tips
- Halve the zeros/places: Count the digits after the decimal. The square root answer will always have exactly half that number of digits after the decimal.