We will see that:
- 0.5*(3/8) is rational
- π*3 is irrational
- 12*√5 is irrational
- (√4)*(1/4) is rational.
Differentiate rational and irrational numbers.
A rational number is a number that can be written as a quotient of integer numbers, while an irrational number is one that can't.
The general rule we will use for this problem is:
- If there is an irrational number in the product, and it does not get canceled, then the product is irrational.
- If there are no irrational numbers in the product, the product is rational.
Here the 4 products are:
1) 0.5*(3/8)
Both of these are rational numbers, as we can write:
0.5 = 1/2
Then the product will give a rational number.
2) π*3
We know that π is an irrational number, thus the product will give an irrational number.
3) 12*√5
Here we have the square root of a prime number, this is an irrational number, thus the product will give an irrational number.
4) (√4)*(1/4)
We can rewrite the product as:
(√4)*(1/4) = 2*(1/4)
So there are no irrational numbers in the product, meaning that the product will give a rational number.
If you want to learn more about rational and irrational numbers, you can read:
https://brainly.com/question/5342576
