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.
Which of the following is an irrational number?(1 point)
Responses
Square root 121/324
Square root 256
3Sqaure root 64
Sqaure root 125
1 answer