if a right angle has a hypotenuse of 19 units and a leg with the length of 7 units, find the length of the other leg
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An irrational number is a real number that can't be written as a fraction: since all rational numbers () are real numbers (
), the irrational numbers are all elements in
that don't belong to
.
The rational numbers are closed with respect to sum and multiplication, which means that the sum/product of two rational numbers is a rational number.
Note that, of all the options, only is irrational, because the other options are
so they all can be written as fraction. This means that
are all rational numbers, because they are the multiplication of two rational numbers.
So, your only hope to get an irrational number is to multiply
Expression 2 works exactly in the same way, because everything we said about the product is true for the sum as well.