Estimate the value of 6×2–√

Question

. Which of the following choices is the best estimate?(1 point)
Responses

8.4
8.4

9.8
9.8

6.4
6.4

7.1

Which statement is true about the square root of 28?(1 point)
Responses

It is between 4 and 5, probably closer to 5.
It is between 4 and 5, probably closer to 5.

It is between 5 and 6, probably closer to 6.
It is between 5 and 6, probably closer to 6.

It is between 6 and 7, probably closer to 6.
It is between 6 and 7, probably closer to 6.

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 point)
Responses

It does not exist.
It does not exist.

It involves large numbers.
It involves large numbers.

It is equal to 1.
It is equal to 1.

It requires a computer to find it.

Answer 1

Let's tackle each question one by one:

1. Estimate the value of 6×2–√.

   • The expression is \(6 \times 2 - \sqrt{2}\).
   • First, calculate \(6 \times 2 = 12\).
   • Next, approximate \(\sqrt{2}\), which is about 1.414.
   • Now, \(12 - 1.414 \approx 10.586\).
   • Based on the choices given, the best estimate is 9.8 (it is indeed underestimating a bit, but it's the closest option to the actual value calculated).

2. Which statement is true about the square root of 28?

   • The exact square root of 28 is approximately 5.291.
   • Therefore, it is true that it is between 5 and 6, probably closer to 5.

3. Which statement is true about the integer fraction that equals the square root of 2?

   • The square root of 2 is an irrational number, meaning it does not exist as a fraction of two integers. Therefore, the correct answer is it does not exist.

So, summarizing the answers:

1. 9.8
2. It is between 5 and 6, probably closer to 5.
3. It does not exist.