How can we rationalize the divisor in division of radicals?

Answer 1

It is easier to describe using an actual example.

Say you have an expression x/sqrt(2). Then multiply by sqrt(2)/sqrt(2) (which is of course equal to 1 and we know that anything multiplied by 1 stays the same. This will get rid of the radical on the bottom.

So the expression becomes x/sqrt(2) * sqrt(2)/sqrt(2) = [x*sqrt(2)]/2 where * means multiply

Answer 2

It depends on the expression. Here are some common examples.* If the entire denominator (or divisor) has a square root, you multiply top and bottom by the same square root. For example, if on the bottom you have the square root of 5, you can multiply top and bottom by the square root of 5.

* If the bottom has an addition, of which one of the terms (or both) is a square root, you multiply top and bottom by the same expression, changing the plus to minus. Similarly, if you have a subtraction, you change minus to plus. For example, if the expression in the denominator is root(3) - root(2), you need to multiply top and bottom by root(3) + root(2).

Answer 3

Multiply both, the numerator and the denominator, of the division by the denominator.