find the square root of the following decimals 387 3.8 176
The correct answer and explanation is:
Let’s find the square roots of the following decimals and numbers:
- √387
- √3.8
- √176
✅ Correct Answers:
- √387 ≈ 19.66
- √3.8 ≈ 1.95
- √176 ≈ 13.27
📘 300-Word Explanation:
Finding the square root of a number means determining what number, when multiplied by itself, gives the original number. For example, since 5 × 5 = 25, the square root of 25 is 5. When dealing with decimals or non-perfect squares like 387, 3.8, and 176, we use either a calculator or estimation followed by refinement.
1. √387
387 is not a perfect square, but we know that 19² = 361 and 20² = 400. Since 387 lies between 361 and 400, √387 must lie between 19 and 20. Using a calculator, we find √387 ≈ 19.66. This means 19.66 × 19.66 ≈ 387.
2. √3.8
This decimal is smaller than 4, whose square root is 2. Since 3.8 is just below 4, its square root should be just below 2. Calculating it gives us √3.8 ≈ 1.95. This means 1.95 × 1.95 ≈ 3.8.
3. √176
Here, 13² = 169 and 14² = 196. 176 is between these two, so √176 is between 13 and 14. Using a calculator, we get √176 ≈ 13.27.
🧠 Why It Matters:
Understanding square roots helps in many areas of math and science, such as geometry, physics, and statistics. It’s especially useful in working with areas, distances, or any quantity involving powers and roots. While perfect squares are easy to calculate mentally, non-perfect squares or decimals often require calculators or approximation methods like the “long division” method or estimation using perfect squares.