Which statement is true about the integer fraction that equals the square root of 2?( 1 point)
Responses:
It involves large numbers.
It does not exist.
It requires a computer to find it.
It is equal to 1.
The statement "It does not exist." is true about the integer fraction that equals the square root of 2.
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.
The statement "It does not exist" is true about the integer fraction that equals the square root of 2.
The correct statement is: "It does not exist."
To understand why this statement is true, let's explore the concept of the square root of 2. The square root of 2 is an irrational number, which means it cannot be expressed as a fraction of two integers.
To verify this, you could try to find a fraction that equals the square root of 2. Assume such a fraction exists as p/q (where p and q are integers). We can square both sides of the equation to get p^2/q^2 = 2. Rearranging the equation, we get p^2 = 2 * q^2.
Considering this equation, notice that the left side (p^2) is an even number because it's the multiple of 2. Therefore, p must also be even (since the square of an odd number is odd). So, we can write p = 2k for some integer k.
Substituting p = 2k back into the equation, we get (2k)^2 = 2 * q^2. Simplifying, we have 4k^2 = 2 * q^2, which can be rewritten as 2k^2 = q^2. This implies that q^2 is an even number since it's the product of 2 and k^2. Consequently, q must also be even.
However, if both p and q are even, they share a common factor of 2. This contradicts the fact that fractions should be reduced to their simplest form, meaning the numerator and denominator should have no common factors apart from 1. Hence, no fraction can exist that equals the square root of 2.
Therefore, the correct statement is that the integer fraction equaling the square root of 2 does not exist.