which of these numbers is irrational
52.781654292
3√/4
-7 8/37
3.6363636363636363...
The number 3√/4 is irrational.
To determine which of these numbers is irrational, we need to understand the definition of an irrational number. An irrational number is any real number that cannot be expressed as a ratio of two integers.
Let's analyze each number to see if it fits this definition:
1. 52.781654292: This number is a decimal. It can be written in the form of a ratio of two integers, such as 5278/100. Therefore, 52.781654292 is not an irrational number.
2. 3√/4: Based on the provided information, it is unclear what exactly you mean by "3√/4." If you meant the cube root of 3 divided by 4 (∛3/4), then this number is irrational. The cube root of 3 cannot be expressed as a ratio of two integers.
3. -7 8/37: This number is a mixed number written in fractional form. Mixed numbers can always be expressed as a ratio of two integers. Therefore, -7 8/37 is not an irrational number.
4. 3.6363636363636363...: This number is a recurring decimal, where the digits "36" repeat indefinitely. Recurring decimals can be expressed as a ratio of two integers. In this case, the decimal 3.636363... can be written as 40/11. Therefore, 3.6363636363636363... is not an irrational number.
Based on the analysis above, the only number that is irrational from the options given is ∛3/4.