The number √4 is rational because __
1. it is a decimal that repeats.
2. It is a decimal that terminates
3. It is a decimal that does not repeat or terminate
4. It is a square root of a perfect square 5. It is a square root of a non-perfect square
4. It is a square root of a perfect square.
The number √4 is rational because it is a square root of a perfect square.
The number √4 is rational because it is a square root of a perfect square.
To understand why, let's first define what a perfect square is. A perfect square is a number that can be expressed as the square of an integer. For example, 4 is a perfect square because it can be expressed as 2² (2 multiplied by itself).
The square root (√) of a number is the value that, when multiplied by itself, gives the original number. In this case, the square root of 4 (√4) is 2, because 2 multiplied by itself equals 4 (2 * 2 = 4).
Now, let's go back to the options given. Option 1 states that √4 is a decimal that repeats. However, when we calculate √4, we get a whole number (2), which does not have any decimal places. Therefore, option 1 is incorrect.
Option 2 states that √4 is a decimal that terminates. A terminating decimal is a decimal number that ends after a certain number of decimal places. But, in this case, √4 equals 2, which does not have any decimal places. So, option 2 is also incorrect.
Option 3 states that √4 is a decimal that neither repeats nor terminates. However, as mentioned before, √4 equals 2, which is a whole number and does not have any decimal places. Hence, option 3 is incorrect.
Option 4 states that √4 is a square root of a perfect square, which is true. As explained earlier, 4 is a perfect square, and √4 equals 2, which is an integer. So, option 4 is correct.
Option 5 states that √4 is a square root of a non-perfect square, which is not true. Since 4 is a perfect square, this option is incorrect.
In summary, the correct answer is option 4. The number √4 is rational because it is a square root of a perfect square.