Explain why the sum, the difference, and the product of two rational numbers are

Josalynn

Josalynn

Answered question

2021-09-08

Explain why the sum, the difference, and the product of two rational numbers are rational numbers. Is the product of two irrational numbers necessarily irrational? What about the sum?

Answer & Explanation

averes8

averes8

Skilled2021-09-09Added 92 answers

Step 1
Consider two rational numbers a/b and c/d.
The sum,the difference and the product of two rational numbers are rational numbers.
=ab+cd
disserence=abcd
uct=ab(cd)
These all are rational numbers because the numbers a,b,c and d are integers.
Step 2
The sum and product of irrational numbers are not always irrational numbers.
For example: Consider two irrational numbers
x=3
y=13
So, the product of these numbers are
x(y)=3(13)=1
which is a rational number.
Now, consider other two irrational numbers
l=π
m=π
So, the sum of these irrational numbers are

l+m=π+(π)=0 which is again rational number.

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