Irrational Fraction
Pro Problems > Math > Logic > Proofs > Indirect ProofsIrrational Fraction
Let a and b be positive integers, with b not a perfect square. Show that the following expression is irrational, using an indirect proof.
bbHint: Remember that an irrational number is a number which cannot be written as the quotient of two integers.
Solution
In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.
Similar Problems
Radical Two Proof
2Hint: An irrational number is a number which cannot be written as the quotient of two relatively prime integers.
A Smaller Fraction
For every positive rational number x, there exists a smaller positive rational number y. Prove this statement by indirect proof.
Sum of Trig Functions
Show that if θ is between 0º and 90º inclusive, then sin θ + cos θ ≥ 1. Use an indirect proof.
X, Y, and Z proof
Prove by contradiction: for any integers x, y, and z with z > 1, x2 - yz2 ≠ z.
Hint: This is a more generalized version of the problem found here: X Squared Proof
X Squared Proof
Prove by indirect method that if x and y are integers, then x2 - 9y ≠ 3.
Harmonic Proof
Create an indirect proof for the following statement: The harmonic mean of any two positive numbers lies inclusively between the two numbers.
Infinite Primes
Use an indirect proof to show that there are infinitely many prime numbers.
Blogs on This Site
Like us on Facebook to get updates about new resources