Find the value of square root 3. 1428 and square root 0.3 14284 up the 3 decimal places
The correct answer and explanation is:
To find the square roots of the numbers provided, we can proceed using either a calculator or manual approximation methods.
1. Square Root of 3.1428
The square root of 3.1428 is approximately: 3.1428≈1.772\sqrt{3.1428} \approx 1.772
To understand this, we begin by recognizing that the square root of a number is the value that, when multiplied by itself, gives back the original number. For 3.1428, this value is roughly 1.772. By squaring 1.772, we get close to 3.1428, confirming that this is an accurate estimate.
Explanation:
- Approximations: Using a method such as long division or a calculator, we can compute the square root of 3.1428. A scientific calculator provides the most precise value.
- Decimal Places: This square root has been rounded to three decimal places for simplicity and practical use.
2. Square Root of 0.314284
The square root of 0.314284 is approximately: 0.314284≈0.561\sqrt{0.314284} \approx 0.561
Similarly, the square root of 0.314284 gives a value of 0.561, which when squared returns a result very close to 0.314284. This value is rounded to three decimal places.
Explanation:
- Square Root Concept: The square root of a number like 0.314284 is the positive value that, when multiplied by itself, yields the original number.
- Approximation: Using a calculator, we get the most accurate value of the square root, which has been rounded to three decimal places.
Why These Approximations Matter:
Square roots are essential for various mathematical calculations and real-world applications, such as physics, engineering, and even in finance. In everyday problems, rounding to a specific number of decimal places—usually 2 or 3—is sufficient to make calculations easier without sacrificing much precision.