The number 0.855555555555555
It is the square root of a perfect square
It is the square root of a non perfect square
It is a decimal that dose not repeat or terminate
The number 0.855555555555555 is not the square root of a perfect square because its decimal representation does not terminate or repeat.
However, it is the square root of a non-perfect square. In fact, if we square 0.855555555555555, we get approximately 0.7333333333333329, which is not a perfect square.
Additionally, as mentioned before, 0.855555555555555 is a decimal that does not repeat or terminate.
To determine whether the number 0.855555555555555 is a square root of a perfect square or a non-perfect square, we can simplify it and check if it can be written as a perfect square.
Step 1: Simplify the decimal:
0.855555555555555 = 85/100
Step 2: Determine if it is a perfect square:
To check whether a number is a perfect square, we need to find its square root. Taking the square root of 85/100 gives us the decimal 0.922.
Step 3: Determine if it is a non-perfect square:
Since 0.855555555555555 is not equal to 0.922 squared, it is not a square root of a perfect square. Therefore, it is a square root of a non-perfect square.
Step 4: Determine if it is a decimal that does not repeat or terminate:
The decimal representation for 0.855555555555555 continues to repeat indefinitely. It is a non-terminating decimal, and the pattern repeats "5" infinitely.
In summary:
- The number 0.855555555555555 is the square root of a non-perfect square.
- It is a decimal that does not terminate but repeats.
To determine whether the number 0.855555555555555 is the square root of a perfect square or a non-perfect square and whether it is a decimal that repeats or terminates, we can follow these steps:
1. Determine if it is the square root of a perfect square:
To find out if a number is the square root of a perfect square, we need to square it. In this case, we would square 0.855555555555555 by multiplying it by itself: 0.855555555555555 * 0.855555555555555 = 0.731712345679012.
Since 0.731712345679012 is not an integer (whole number), the number 0.855555555555555 is not the square root of a perfect square.
2. Determine if it is the square root of a non-perfect square:
If a number is not the square root of a perfect square, it is the square root of a non-perfect square. Therefore, we can conclude that 0.855555555555555 is the square root of a non-perfect square.
3. Determine if it is a decimal that repeats or terminates:
A decimal that repeats is called a repeating decimal, while a decimal that terminates ends or stops after a certain number of digits. To determine if 0.855555555555555 is a repeating or terminating decimal, we can examine the decimal representation.
In this case, we notice that the number 5 repeats repeatedly after the decimal point. Therefore, 0.855555555555555 is a decimal that repeats.
In summary:
- The number 0.855555555555555 is the square root of a non-perfect square.
- It is a decimal that repeats.