Find the square root of 7.3 upto 3 decimal places.
The correct answer and explanation is:
Correct Answer:
The square root of 7.3 up to three decimal places is 2.702.
Explanation (300 words):
Finding the square root of a number involves determining a value that, when multiplied by itself, gives the original number. In this case, we are looking for the square root of 7.3, which is not a perfect square. This means its square root will be an irrational number—a non-repeating, non-terminating decimal.
To find the square root up to three decimal places, we can use several methods:
- Estimation and successive approximation
- Long division method
- A calculator (for speed and precision)
Using a Calculator:
The quickest and most accurate method is using a scientific calculator or a programming tool. Inputting √7.3 gives: 7.3≈2.7018512…\sqrt{7.3} ≈ 2.7018512…
When rounding to three decimal places, we look at the fourth digit after the decimal:
- The first three digits: 2.701
- The next digit is 8, which is greater than 5, so we round up the last digit
Thus: 7.3≈2.702\sqrt{7.3} ≈ \boxed{2.702}
Using Estimation:
We know:
- √4 = 2
- √9 = 3
So √7.3 lies between 2 and 3.
Try:
- 2.7² = 7.29
- 2.71² = 7.3441 (too high)
- So the value must be between 2.7 and 2.71
Refining further:
- 2.705² = 7.316025
- 2.702² = 7.304804 (very close to 7.3)
So by iterating this way, we also arrive at 2.702.
Conclusion:
The square root of 7.3, accurate to three decimal places, is 2.702. This level of precision is often sufficient in science, engineering, and finance unless extremely high accuracy is needed.