Irrational Numbers

1. Definition of Root Form in Math

The root form is the root of a number whose value is an irrational number.

2. Simplifying Way of Root Form

The root form can be simplified by changing the number in the root into two numbers where one number can be rooted, while the other can not be rooted.

Example:
√32 = √(16 x 2)
√32 = √16 x √2
√32 = 4 x √2
√32 = 4√2

3. Operate Root Form

a. Addition and Reduction Root Form

Root form can be summed or subtracted if its roots are similar..

Example:

b. Integers Multiplication with Root Form

a x b√c = ab√c

Example:
4 x 3√2 = (4 x 3)√2
4 x 3√2 = 12√2

c. Multiplication of Root Form with Root Form

√a x √b = √(a x b)

a√c x b√d = a x b √(c x d)

√a x √a = a

(√a + √b)(√a - √b) = a - b

Example:
√3 x √2 = √(3 x 2)
√3 x √2 = √6

d. Division of The Root Form

The simplification of the division of root forms is often referred to as the "rationalizing denominator" of fractional forms.

To rationalize the denominator of the fraction, look at the formula below: