Which of the following is a rational number? (5 points)
square root of 2, square root of 3, square root of 4, and square root of 5
square root of 2
square root of 3
square root of 4
square root of 5
The square root of 4 is a rational number.
A rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero.
Out of the given options:
- The square root of 2 is irrational because it cannot be expressed as a ratio of two integers.
- The square root of 3 is also irrational and cannot be expressed as a ratio of two integers.
- The square root of 4 is rational because it equals 2, which can be expressed as a ratio of two integers (2/1).
- The square root of 5 is irrational and cannot be expressed as a ratio of two integers.
Therefore, the only rational number among the options is the square root of 4.
To determine which of the given numbers are rational, we need to understand what a rational number is. A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.
Let's examine each number:
- The square root of 2 (√2) is an irrational number, meaning it cannot be expressed as a fraction of two integers.
- The square root of 3 (√3) is also an irrational number.
- The square root of 4 (√4) is equal to 2. Since 2 can be expressed as the fraction 2/1, it is a rational number.
- The square root of 5 (√5) is another irrational number.
Therefore, out of the given numbers, only the square root of 4 (√4) is a rational number.