Which statement is true about the integer fraction that equals the square root of 2?(1 point)
Responses
It requires a computer to find it.
It requires a computer to find it.
It does not exist.
It does not exist.
It involves large numbers.
It involves large numbers.
It is equal to 1.
It does not exist.
Which statement is true about the square root of 28?(1 point)
Responses
It is between 5 and 6, probably closer to 5.
It is between 5 and 6, probably closer to 5.
It is between 4 and 5, probably closer to 5.
It is between 4 and 5, probably closer to 5.
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 6.
It is between 5 and 6, probably closer to 6.
It is between 5 and 6, probably closer to 6.
Estimate the value of 6×2–√. Which of the following choices is the best estimate?(1 point)
Responses
7.1
7.1
8.4
8.4
6.4
6.4
9.8
The best estimate for 6×2–√ is 6.4.
The statement "It involves large numbers" is true about the integer fraction that equals the square root of 2.
The statement "It is equal to 1" is true about the integer fraction that equals the square root of 2.
To understand why this statement is true and how to find the answer, let's break it down step by step:
1. The square root of 2 (√2) is an irrational number, which means it cannot be expressed as a simple fraction or a decimal that terminates or repeats. It goes on infinitely without a pattern.
2. However, we can approximate the square root of 2 using decimal numbers. For example, √2 is approximately equal to 1.41421356.
3. The term "integer fraction" refers to a fraction where both the numerator and denominator are integers. In other words, we need to find a fraction of the form a/b, where a and b are both whole numbers.
4. By examining the decimal approximation of √2 (1.41421356), we can see that if we take the fraction 1/1, it is close to √2 but slightly smaller.
5. If we multiply both the numerator and denominator of the fraction 1/1 by √2, we get (√2)/√2, which is equal to (√2 * √2) / (√2) = 2/√2.
6. To simplify 2/√2 and make the denominator an integer, we need to rationalize the denominator by multiplying both the numerator and denominator by √2. This gives us (2√2) / (√2 * √2) = (2√2) / 2 = √2.
7. Therefore, √2 can be represented as the fraction √2 = (2√2) / 2. Since both the numerator (2√2) and denominator (2) are integers, we can say that the integer fraction that equals the square root of 2 is 2/2, which simplifies to 1.
In conclusion, the statement "It is equal to 1" is true about the integer fraction that equals the square root of 2.