Asked by hola
Which number is irrational?
Responses
6√
square root of 6
13
1 over 3
0.14¯¯¯¯
0.14 with bar over 1 4
4√
Responses
6√
square root of 6
13
1 over 3
0.14¯¯¯¯
0.14 with bar over 1 4
4√
Answers
Answered by
GPT-4o mini
To determine which number is irrational, let's evaluate each option:
1. **6√**: This expression seems incomplete, but if it's intended to mean \( 6\sqrt{a} \) where \( a \) is a positive integer that isn't a perfect square (like 6), then it could be irrational. However, if it represents \( 6\sqrt{6} \), this too would be irrational because the square root of a non-perfect square is irrational.
2. **Square root of 6**: This is indeed an irrational number because 6 is not a perfect square.
3. **13**: This is a whole number and is rational.
4. **1 over 3**: This is \( \frac{1}{3} \), which is also a rational number.
5. **0.14¯¯¯¯ (0.14 with a bar over 14)**: This represents the repeating decimal 0.141414…, which is a rational number.
Based on this analysis, the **square root of 6** is the only irrational number listed.
1. **6√**: This expression seems incomplete, but if it's intended to mean \( 6\sqrt{a} \) where \( a \) is a positive integer that isn't a perfect square (like 6), then it could be irrational. However, if it represents \( 6\sqrt{6} \), this too would be irrational because the square root of a non-perfect square is irrational.
2. **Square root of 6**: This is indeed an irrational number because 6 is not a perfect square.
3. **13**: This is a whole number and is rational.
4. **1 over 3**: This is \( \frac{1}{3} \), which is also a rational number.
5. **0.14¯¯¯¯ (0.14 with a bar over 14)**: This represents the repeating decimal 0.141414…, which is a rational number.
Based on this analysis, the **square root of 6** is the only irrational number listed.