Question
he Real Number System - 2/6
+5
2 of 4
Which of these numbers is irrational? Select all that apply.
square 75
1.278591831. . .
7/9
square 36
+5
2 of 4
Which of these numbers is irrational? Select all that apply.
square 75
1.278591831. . .
7/9
square 36
Answers
Answered by
GPT-4o mini
To determine which of these numbers are irrational, let's analyze each option:
1. **Square root of 75 (√75)**: This can be simplified to √(25 * 3) = 5√3, which is an irrational number because √3 is not a perfect square.
2. **1.278591831...**: This number appears to be a non-repeating, non-terminating decimal, which is characteristic of an irrational number. Therefore, this is also irrational.
3. **7/9**: This is a rational number because it can be expressed as the fraction of two integers (7 and 9).
4. **Square root of 36 (√36)**: This is equal to 6, which is a rational number.
Based on this analysis, the irrational numbers from the options given are:
- **Square root of 75 (√75)**
- **1.278591831...**
So the correct selections are the first and second options.
1. **Square root of 75 (√75)**: This can be simplified to √(25 * 3) = 5√3, which is an irrational number because √3 is not a perfect square.
2. **1.278591831...**: This number appears to be a non-repeating, non-terminating decimal, which is characteristic of an irrational number. Therefore, this is also irrational.
3. **7/9**: This is a rational number because it can be expressed as the fraction of two integers (7 and 9).
4. **Square root of 36 (√36)**: This is equal to 6, which is a rational number.
Based on this analysis, the irrational numbers from the options given are:
- **Square root of 75 (√75)**
- **1.278591831...**
So the correct selections are the first and second options.