Which is irrational?
Responses
−14.7
negative 14 point 7
34
3 fourths
27−−√
square root of 27
81−−√
square root of 81
81−−√ (the square root of 81) is irrational.
To determine which of the given options is irrational, we should understand what irrational numbers are.
An irrational number is a number that cannot be expressed as a fraction or ratio of two integers. It is a number that goes on forever without repeating decimal places. Examples of such numbers are π (pi) and √2 (the square root of 2).
Now, let's analyze each option:
Option 1: −14.7 or negative 14.7
This number can be written as a ratio of two integers (-147/10) since it is a terminating decimal. Therefore, it is not an irrational number.
Option 2: 34 or 3/4
This number is a whole number and can be expressed as the ratio of two integers (34/1 or 68/2). Hence, it is not an irrational number.
Option 3: 27−√ or square root of 27
The square root of 27 is an irrational number since it cannot be expressed as a fraction or ratio of two integers. The decimal representation of the square root of 27 goes on forever without repeating.
Option 4: 81−√
The square root of 81 is not an irrational number because it can be expressed as a whole number (9). It is equal to 9/1 or 18/2 written as a ratio of two integers.
Therefore, based on the analysis, the only option that is irrational is the square root of 27, written as 27−√.