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.
