Can someone help me reword these two things? I don't like how I did them but I can't think of anything else. Thanks!!
1. PROMPT: What do you do to check whether a number is rational or irrational? In your explanation, use an example of an irrational and a rational number.
My answer that needs reworded: Any number that can be expressed as a fraction of the form a/b, where b is not equal to 0, is rational. A number that can't be expressed as a fraction in the form a/b is irrational.
Decimals which terminates is rational.
Decimals which repeats is rational.
Decimals which doesn't show any repeating decimals and which is never-ending is irrational.
Examples:
5/8 - rational
2.252525... rational
5.878787.. rational
9.895043... irrational
pi - irrational
√5 or any square root of a number which isn't a perfect square is irrational.
√16 -- rational, but √17 -- irrational.
2. PROMPT: How does finding the square root of a number compare to finding the cube root of a number? Use the number 64 in your explanation.
My answer that needs reworded: To find the square root, you would want to find the number y as in y x y = 64. y = 8.
To find the cube root, you want to find the number z as in z x z x z = 64. z = 4.
If the root is not a perfect fit, then you have to use a numeric method to approximate the value.
Thanks loves!! <3
In other words you did not mention that if the numbers repeat it is rational and even if with some difficulty a whole numerator and denominator can be found.
9.895043895043895043895043895043895043 ............ :)
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bot?
1. To determine whether a number is rational or irrational, you can check if it can be expressed as a fraction in the form of a/b, where b is not equal to 0. For example, decimals that terminate or repeat are considered rational, while decimals that neither terminate nor repeat are considered irrational.
Here are some examples:
- 5/8 is a rational number.
- Decimals like 2.252525... or 5.878787... that repeat are rational.
- However, decimals like 9.895043... that neither terminate nor repeat are considered irrational.
- π (pi) is another example of an irrational number.
Additionally, any square root of a number that is not a perfect square will also be irrational. For instance, √5 or any other square root of a non-perfect square is irrational. On the other hand, the square root of a perfect square like √16 is rational, while the square root of a non-perfect square like √17 is irrational.
2. When finding the square root of a number, you are looking for the number that, when multiplied by itself, equals the given number. For instance, to find the square root of 64, you would try to find the number y such that y x y = 64. In this case, y is equal to 8.
On the other hand, when finding the cube root of a number, you are searching for the number that, when multiplied by itself three times, equals the given number. Using the number 64 as an example, you would find the number z such that z x z x z = 64. In this case, z is equal to 4.
If the desired root (square root, cube root, etc.) is not an exact whole number, you may need to use numerical approximation methods to find an approximate value.
I hope this helps! Let me know if you have any further questions.