Which of the following is an irrational number: 25−−√, π, or 027? (1 point)
The irrational number among the given options is π.
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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)
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which of the following is an irrational number between 5 and 7: 6–√, 12−−√, 27−−√, 36−−√?
To determine which of the following numbers is irrational, we need to understand the definition of irrational numbers.
An irrational number is a real number that cannot be expressed as a simple fraction or ratio of two integers. It cannot be written as a terminating decimal or a repeating decimal.
Let's analyze each of the given numbers:
1. 25−√: This is the square root of 25. Since 25 is a perfect square (5 * 5), its square root is a rational number. Therefore, 25−√ is not an irrational number.
2. π (pi): Pi is an irrational number that represents the ratio of a circle's circumference to its diameter. It is approximately equal to 3.14159 and continues indefinitely without a pattern. So, π is an irrational number.
3. 027: This number is an integer, specifically 27 written in decimal notation. Integers are rational numbers because they can be expressed as fractions where the denominator is 1. Therefore, 027 is not an irrational number.
In conclusion, the irrational number among the given options is π.