what is the square root of 40 the values to the nearest hundredth
The correct answer and explanation is:
✅ Correct Answer:
The square root of 40 to the nearest hundredth is:
√40 ≈ 6.32
🧠 Explanation (300 words):
The square root of a number refers to the value that, when multiplied by itself, gives the original number. In this case, we are finding the number that, when squared, equals 40. Mathematically, this is represented as: 40=xsuch thatx2=40\sqrt{40} = x \quad \text{such that} \quad x^2 = 40
1. Understanding the Problem:
40 is not a perfect square (like 36 or 49), so its square root will not be a whole number. Instead, it will be a decimal. The goal is to find this decimal value to the nearest hundredth, which means rounding it to two decimal places.
2. Estimate Between Perfect Squares:
We can start by estimating between two perfect squares:
- √36 = 6
- √49 = 7
So, √40 lies between 6 and 7.
Now try refining further:
- 6.32=39.696.3^2 = 39.69
- 6.42=40.966.4^2 = 40.96
Since 40 is between these, try:
- 6.312=39.81616.31^2 = 39.8161
- 6.322=39.94246.32^2 = 39.9424
- 6.332=40.06896.33^2 = 40.0689
Here, 6.322≈39.946.32^2 ≈ 39.94 is closest to 40 without exceeding it.
So, √40 ≈ 6.32
3. Why This Matters:
Square roots are widely used in geometry, algebra, physics, and real-world calculations like measuring distances, calculating areas, and working with quadratic equations. Approximating square roots is essential when working without a calculator or when estimating is more practical than using exact values.
Knowing how to estimate or calculate square roots also improves your understanding of number patterns and mathematical reasoning. It’s especially useful in science and engineering fields where precision matters.
Final Answer: √40 ≈ 6.32 (to the nearest hundredth) ✅