Which of the following is an irrational number?(1 point)
Responses
Square root 121/324
Square root 256
3Sqaure root 64
Sqaure root 125
To identify which of the following is an irrational number, we need to understand that an irrational number is a number that cannot be expressed as a simple fraction – it's a number that cannot be written as a ratio of two integers. Irrational numbers have non-repeating, non-terminating decimal parts.
Let's examine your options:
1. Square root of 121/324
This can be simplified into two separate square roots: the square root of 121, which is 11, and the square root of 324, which is 18. So we have 11/18, which is a rational number because it can be expressed as a fraction of two integers.
2. Square root of 256
The square root of 256 is 16, which is a rational number since it's an integer.
3. 3 Square root of 64
Here we have 3 times the square root of 64, which is 3 * 8 = 24, and again this is a rational number because it's an integer.
4. Square root of 125
The square root of 125 cannot be simplified to a whole number or a perfect fraction. 125 is not a perfect square (unlike 121, 256, or 64), so taking the square root of 125 results in a non-repeating, non-terminating decimal. Thus, the square root of 125 is an irrational number.
Therefore, out of the options given, the square root of 125 is the irrational number.