what is the square root of 481
The correct answer and explanation is:
✅ Correct Answer:
The square root of 481 is approximately 21.93.
📘 Explanation (Approximately 300 Words):
The square root of a number is a value that, when multiplied by itself, gives the original number. In mathematical terms: 481=xsuch thatx2=481\sqrt{481} = x \quad \text{such that} \quad x^2 = 481
Let’s break this down.
Step 1: Estimate the Square Root
We start by estimating. We know:
- 202=40020^2 = 400
- 222=48422^2 = 484
So, the square root of 481 must be between 21 and 22, because: 212=441and222=48421^2 = 441 \quad \text{and} \quad 22^2 = 484
481 is closer to 484 than to 441, so the square root is closer to 22.
Step 2: Refine the Estimate
Try 21.9: 21.92=479.61(too low)21.9^2 = 479.61 \quad (\text{too low})
Try 22.0: 22.0^2 = 484 \quad (\text> too high})
Try 21.93: 21.932=480.9249≈481(very close)21.93^2 = 480.9249 \approx 481 \quad (\text{very close})
So, the square root of 481 ≈ 21.93.
Step 3: Check with a Calculator
To confirm, use a calculator: 481≈21.9317\sqrt{481} \approx 21.9317
Rounded to two decimal places: 21.93
🔍 Additional Insights
- 481 is not a perfect square, because its square root is not a whole number.
- If a number ends in 1, like 481, it could be a perfect square, but we must check.
- Perfect squares near 481 include 441 (21²) and 484 (22²).
- Square roots are often used in geometry (e.g., finding the length of the hypotenuse) and in statistics (e.g., standard deviation).
✅ Final Answer:
481≈21.93\boxed{\sqrt{481} \approx 21.93}