Which is irrational?
Responses
81−−√
square root of 81
−14.7
negative 14 point 7
34
3 fourths
27−−√
The irrational number is √81.
The irrational number among the given options is the square root of 81, denoted as 81√.
To determine which number is irrational among the given options, let's recall the definition of an irrational number. An irrational number is a number that cannot be expressed as a fraction or ratio of two integers.
Let's analyze each option to determine if it meets this criteria:
1. √81: The square root of 81 is 9 because 9 * 9 = 81. Since 9 can be expressed as a ratio of two integers (9/1), it is a rational number.
2. -14.7: -14.7 is a decimal representation of a rational number. Even though it is not an integer, it can still be written as a fraction (-147/10), therefore it is rational.
3. 34: 34 is an integer, and every integer can be written as a fraction by dividing it by 1. Hence, it is rational.
4. √27: The square root of 27 is approximately 5.196. When we try to express this number as a fraction, we find that there is no combination of integers that can represent it. Therefore, the square root of 27 is an irrational number.
Based on this analysis, the number √27 (square root of 27) is the irrational number among the given options.