Estimate the value of 6×2–√. Which of the following choices is the best estimate?(1 point)
Responses:
9.8
8.4
7.1
6.4
I do not know what or who you are BOT... But people should be careful, as IT gives different answers every time! This is another answer Bot gave:
"To estimate the value of 6×2–√, we can calculate the square root of 2, which is approximately 1.41, and then multiply it by 6.
6 × 1.41 ≈ 8.46
Therefore, the best estimate would be 8.4.
DO YOUR WORK AND BE CAREFUL OF THIS "THING"!
To estimate the value of 6×2–√, we can follow these steps:
1. Calculate 6×2: 6×2 = 12.
2. Subtract the square root: 12 – √ ≈ 12 – 1.4.
Therefore, the best estimate for 6×2–√ is 10.6.
None of the given choices match this estimate.
To estimate the value of 6×2–√, we can break it down into steps.
Step 1: Simplify 6×2–√.
Since the square root sign (√) is written without a number inside it, we assume it means the square root of the previous number. So, 6×2–√ means 6 multiplied by the square root of 2.
Step 2: Estimate the square root of 2.
The exact value of the square root of 2 is an irrational number (approximately 1.41421356), but for estimation purposes, we can round it to a more manageable decimal. In this case, we can round it to around 1.4.
Step 3: Multiply 6 by the estimate of the square root of 2.
6 multiplied by 1.4 is approximately 8.4.
Now, looking at the available responses:
9.8
8.4 (This is our estimation)
7.1
6.4
We can see that the best estimate for 6×2–√ is 8.4.
To evaluate 6×2–√, we can first solve the square root term: √2 ≈ 1.41.
Next, we can substitute this value into the equation: 6×2–√ ≈ 6×2–1.41 ≈ 6×2–1.4 ≈ 12–1.4 ≈ 10.6.
Therefore, the best estimate from the given choices is 9.8.