1) What do you do to check whether a number is rational or irrational? Use an example of a rational and an irrational number.
2) How does finding the square root [√] of a number compare to finding the cube root [^3√] of a number? Use the number 64 in your explanation.
PLEASE EXPLAIN!
I already finished with 1)
I really need help with number two though!
Sorry about the long name
8 * 8 = ?
4 * 4 * 4 = ?
1) To determine whether a number is rational or irrational, you need to understand their definitions.
- A rational number is any number that can be expressed as a fraction (where the numerator and denominator are integers). Rational numbers can also be written as terminating or repeating decimals.
Example: 2/3 or 0.75
- An irrational number is a number that cannot be expressed as a fraction and whose decimal representation neither terminates nor repeats. Irrational numbers often involve non-recurring and non-terminating decimals.
Example: √2 or π (pi)
Now, let's use an example to check whether a number is rational or irrational:
Consider the number √9.
First, determine if √9 can be written as a fraction (i.e., in the form a/b). Since the square root of 9 is 3, we can express it as 3/1, which is indeed a fraction. Therefore, √9 is a rational number.
Next, let's consider the number √7.
Can √7 be expressed as a fraction? No matter how hard we try, it is impossible to simplify or write √7 as a fraction. Therefore, √7 is an irrational number.
2) Finding the square root (√) and the cube root (^3√) of a number differ based on the power to which we raise the number for the radical operation.
- Square root (√): It involves finding the value that, when multiplied by itself, gives the original number. For example, let's find the square root of 64 (√64). By multiplying 8 by itself (8 * 8 = 64), we get the desired value. So √64 = 8.
- Cube root (^3√): It involves finding the value that, when multiplied by itself two more times, gives the original number. Consider the cube root of 64 (^3√64). By multiplying 4 by itself twice (4 * 4 * 4 = 64), we obtain the desired value. Therefore, ^3√64 = 4.
In summary, the square root (√) is finding the number that, when squared, gives the original number, while the cube root (^3√) is finding the number that, when cubed, gives the original number.
Please use a much, much shorter name for your posts.
http://www.mathsisfun.com/irrational-numbers.html
What do you think the answer for 2 is?