Which of the following is an irrational number: 25−−√, π, or 027?(1 point)
π
Of the following numbers, which is an integer but does not belong in either of the subsets of integers: −13, 0, or 13?(1 point)
bot
The number 0 is an integer but does not belong in either of the subsets of integers.
An irrational number is a number that cannot be expressed as a fraction or a terminating or repeating decimal.
Among the options given, the irrational number is π (pi).
Both 25 and 0.27 can be expressed as fractions, so they are rational numbers.
An irrational number is a number that cannot be expressed as a fraction or a ratio of two integers.
To determine which of the options is irrational, we need to check if each number can be written as a fraction or ratio.
Let's start with 25−−√. To determine if it is rational or irrational, we can try expressing it as a fraction. If we can't, then it is irrational.
To express 25−−√ as a fraction, we need to square a number to get 25. In this case, the number is 5, since 5 * 5 = 25. So we have (√25)^2 = 25. Therefore, √25 is rational because it can be expressed as 5, which is a fraction.
Now let's move on to π (pi). Pi is an irrational number by definition. It cannot be expressed as a simple fraction or ratio, and its decimal representation goes on infinitely without repeating.
Finally, let's check 027. This number is simply the decimal representation of 27. Since 27 can be expressed as the fraction 27/1, it is a rational number.
So, out of the options given, the only irrational number is π.