A water tank holds 486 gallons but leaking at a rate 4 gallons per week. A second water tank holds 648 gallons but is leaking at
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We have to prove that is irrational. We can prove this statement by contradiction.
Let us assume that is a rational number. Therefore, we can express:
Let us represent this equation as:
Upon squaring both the sides:
Since a has been assumed to be rational, therefore, must as well be rational.
But we know that is irrational, therefore, from equation
the expression
must be irrational, which contradicts with our claim.
Therefore, by contradiction, is irrational.