Estimate the value of 6×2–√. Which of the following choices is the best estimate?
1. 9.8
2. 7.1
3. 6.4
4. 8.4
To estimate the value of 6×2–√, we can calculate each term separately and then subtract.
First, calculate 6×2: 6×2 = 12.
Next, calculate the square root of 12: √12 ≈ 3.464 (rounded to three decimal places).
Finally, subtract the square root of 12 from 12: 12 - √12 ≈ 8.536 (rounded to three decimal places).
Therefore, the best estimate for the value of 6×2–√ is 8.5.
Among the answer choices provided, the best estimate is 8.4 (option 4).
Which statement is true about the square root of 28?
1. It is between 4 and 5, probably closer to 5.
2. It is between 6 and 7, probably closer to 6.
3. It is between 5 and 6, probably closer to 6.
4. It is between 5 and 6, probably closer to 5.
To estimate the value of the square root of 28, we can consider the perfect squares closest to 28, which are 25 and 36.
The square root of 25 is 5, and the square root of 36 is 6. Therefore, the square root of 28 is between 5 and 6.
Since 28 is closer to 25 than it is to 36, the square root of 28 is probably closer to 5 than it is to 6.
Therefore, the statement that is true about the square root of 28 is:
4. It is between 5 and 6, probably closer to 5.
Which statement is true about the integer fraction that equals the square root of 2?
1. It requires a computer to find it.
2. It is equal to 1.
3. It involves large numbers.
4. It does not exist.
The statement that is true about the integer fraction that equals the square root of 2 is:
4. It does not exist.
The square root of 2 is an irrational number, which means it cannot be expressed as a fraction of two integers. It is a non-repeating and non-terminating decimal. Therefore, there is no integer fraction that equals the square root of 2.
To estimate the value of 6×2–√, we need to evaluate the expression step-by-step.
Step 1: Evaluate 6×2
6×2 = 12
Step 2: Take the square root of 12
√12 ≈ 3.46 (rounded to two decimal places)
Step 3: Subtract the square root from 12
12 - 3.46 ≈ 8.54 (rounded to two decimal places)
Based on the steps above, the best estimate for 6×2–√ is approximately 8.54.
Among the given choices, the closest value to the estimate is 8.4 (option 4). Therefore, option 4, 8.4, is the best estimate.
To estimate the value of 6×2-√, we need to evaluate the expression step by step.
Step 1: Evaluate the square root (√)
To do this, we need to find the square root of the number inside the square root symbol. In this case, there is no number provided, so we cannot evaluate it accurately. Therefore, we will leave the expression as 6×2-√.
Step 2: Evaluate the multiplication (×)
Next, we need to multiply 6 by 2. This gives us 12. So the expression becomes 12-√.
Since we cannot accurately evaluate the square root (√), we keep it as it is.
Based on these steps, we can say that the best estimate for the value of 6×2-√ is 12-√.
Looking at the given choices:
1. 9.8
2. 7.1
3. 6.4
4. 8.4
None of these options accurately represent the value of 6×2-√, as we cannot accurately evaluate the square root (√) without more information. Therefore, none of the given choices is a suitable estimate for the expression 6×2-√.