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Root Rules

Introduction:

Introduction:

In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square (the result of multiplying the number by itself) is x. Every non-negative real number x has a unique non-negative square root, called the principal square root, denoted by a radical sign as . For positive x, the principal square root can also be written in exponent notation, as x1/2. For example, the principal square root of 9 is 3, denoted, because 32 = 3 3 = 9 and 3 is non-negative. Source: Wikipedia.

Root Rules with their Examples

Root Rule 1:

p=q if both q>= 0 q2 =p.

Example: 16 =4 because 42 =16.

Here 16 can be written as 4 x 4. so square root of 16 is 4

Root Rule 2:

x2 =|x|

Example: (-6)2 =|-36| =36

Each and every absolute values are always positive.

Root Rule 3:

If p>=0 then p2 = p

Example :112 =121

Here 121 can be expressed as 11 x 11 so the square root of 121 is 11

Root Rule 4:

(pq) = p q

here p>=0 and q>=0

Example:

15 =5 x 3

Root Rule 5:

'(p)/(q)' =p/q

here p>=0 and q>=0 here b is not equal to zero

Example:

25/9 =25 / 9 =5/3

Here square root of 25 is 5 and then square root of 9 is 3 so the answer is 5/3

Root Rule 6:

x xx =x Here x is >= 0

Example :

15 x 15 =15

Multiples of same square root of a number results that number only.

Root Rule 7:

pn =(p)n

Example :

32 =(3)2

Root Rule 8:

p + q is not equal to (p+q)

Example:

2 + 3 is not equal to 5

Sum of separate root of square root numbers is not equal to their sum of the square root number.

Root Rule 9:

p - q is not equal to (p-q)

Example:

4 - 3 is not equal to 1

Difference of separate root of square root numbers is not equal to their difference of the square root number.

Root Rule 10:

(p2 + q2 ) is not equal to p+q

Example:

(32 + 22 ) is not equal to 3+2 that is 5

These are the main important rules that are used in the expression and equations.

by: jeri
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