What is the Square root of 485?
The Correct Answer and Explanation is:
√485 ≈ 22.0227
Explanation
The square root of 485 is approximately 22.0227. This value is not a whole number because 485 is not a perfect square. A perfect square is a number that is the square of an integer (like 1, 4, 9, 16, 25, etc.). In this case, 22² = 484 and 23² = 529, so √485 lies between 22 and 23.
Step-by-Step Estimation:
- Identify perfect squares near 485:
- 22² = 484
- 23² = 529
- Refine the estimate:
We can use the method of averaging or a calculator to get a more accurate result. Using a calculator: 485≈22.0227\sqrt{485} \approx 22.0227
Understanding the Square Root:
A square root of a number is a value that, when multiplied by itself, gives the original number. So in this case: 22.0227×22.0227≈48522.0227 \times 22.0227 \approx 485
This means 22.0227 is a number that satisfies the equation: x2=485x^2 = 485
Applications and Relevance:
Knowing how to approximate or calculate square roots is useful in fields like geometry, physics, engineering, and statistics. For instance, square roots are used to calculate the length of the diagonal of a square, in solving quadratic equations, or in computing standard deviations in data analysis.
Final Note:
While √485 doesn’t yield a neat, whole-number result, understanding how to estimate or compute it accurately is a key mathematical skill. You can use calculators, estimation techniques, or algorithms like the Babylonian method to find such square roots manually if needed.
