Question

p.t ✓234 is irrational

Answer 1

An irrational number is a number that is NOT rational. It cannot be expressed as a fraction with integer values in the numerator and denominator. 

When an irrational number is expressed in decimal form, it goes on forever without repeating.

Proof that the square root of 2 is irrational. 

Assume √2 is rational, i.e. it can be expressed as a rational fraction of the form b/a where a and b are two relatively prime integers.

Now, since √2=b/a we have 2=b2/a2
Since 2a2 is even,  b2 must be even, and since b2 is even, so is a2.
However, two even numbers cannot be relatively prime, so cannot be expressed as a rational fraction; hence  √2 is irrational.

Answer 2

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