Definition: An irrational number is a real number that cannot be written as a fraction of two integers, so its decimal never ends and never repeats.
What is an irrational number?
It is a number that is not rational. No integer fraction equals it exactly, and its decimal digits go on forever with no repeating block.
Which numbers are irrational?
The square root of any whole number that is not a perfect square, such as the square root of 2 (about 1.41421) or the square root of 7 (about 2.64575). Also pi (about 3.14159). Square roots of perfect squares, like the square root of 49, equal 7, so they are rational.
How do you estimate one?
Bracket it between perfect squares. Since 25 < 28 < 36, the square root of 28 lies between 5 and 6. Because 5.3 squared is 28.09, it is close to 5.29.
How do you place it on a number line?
Plot its decimal approximation. The square root of 10, about 3.16, is a little past 3.
What is a common mistake?
Treating a rounded decimal as exact. The value 1.414 is rational, but the square root of 2 is not. Also, the sum of a rational and an irrational is irrational, for example 3 + the square root of 5.