Which of the following is the best approximation of 10 times the positive square root of 20?
A.
100.0
B.
44.7
C.
200.0
D.
89.4
The correct answer and Explanation is :
Let’s break this down step by step to find the best approximation of 10 times the positive square root of 20.
Step 1: Find the square root of 20
To calculate the square root of 20, we use a calculator or approximate manually. We know that:
[
\sqrt{16} = 4 \quad \text{and} \quad \sqrt{25} = 5
]
Since 20 is between 16 and 25, its square root will be between 4 and 5. By using a calculator:
[
\sqrt{20} \approx 4.472
]
Step 2: Multiply by 10
Next, multiply the square root of 20 by 10:
[
10 \times \sqrt{20} = 10 \times 4.472 = 44.72
]
Step 3: Compare with the answer choices
Now, we compare our calculated value (44.72) to the given options:
- A. 100.0
- B. 44.7
- C. 200.0
- D. 89.4
The closest option is B. 44.7.
Explanation:
The square root of 20 is a value between 4 and 5, which we calculated as approximately 4.472. When multiplied by 10, this gives us about 44.72. The correct approximation is 44.7.
- Option A (100.0) and Option C (200.0) are much larger than the correct value.
- Option D (89.4) is roughly double the correct answer, so it’s also incorrect.
Therefore, the correct answer is B. 44.7. This method of approximation uses both a rough estimate and a calculator-based precise value to ensure accuracy.