Rational numbers terminate (1,2,3,....) or repeat (1/3 or .3333333...). Irrational numbers never terminate or repeat.  Perhaps the most common irrational number is Pi. Additionally, the square root of any number that is not a perfect square is irrational (square root of 2, square root of 3, square root of 5, etc.)  

Rational comes from the … Read more

Pi is an irrational number because it never terminates or repeats.

Tangent is sine over cosine.  At 60 degrees sine (the y value) is square root 3 over 2, cosine (the x value) is 1/2.  Since tangent is sine/cosine you would divide square root 3 / 2 by 1/2.  Using the basics of dividing fractions multiply square root 3/2 by the reciprocal of 1/2 which is 2/1 (Some people … Read more