Purpose Of Surds
As we know the numbers like √9, √16, √49 or √225, all of these roots give answers like 3,4,7 and 25, These Kind of roots are considered easy and normal to calculate
Square roots like √2, √13, √41,√113, all of these give answers that are long in decimals or are rational or irrational numbers, This is where we use surds
Surds are useful here as representing irrational numbers like √2 = a/b or a√b, surds can also be represented in a exponential way like root,cube, 4 as a exponent and also up to any number you name, square roots are mostly used to understand what surds are.
Multiplication Rule
The X rule talks about the multiplication of surds and there rules
Example : √6 x √5 can be defined as √6x5 which results to √30, if we take the √12, we can define it as √6x2 which is similar to √6 x √2
Division Rule
The division rule talks about division of surds and there rules
Example : √24/√8 can also be written as √24/8, as a whole, the answer will be written as √3
Addition Rule
The rule of addition talks about addition in surds and there rules
Example : The rule of addition is simple like √7 + √3 can be written as √7+3 but you can't write the answer as √10 as it will result in a wrong way
Subtraction Rule
The subtraction rule talks about subtraction through surds and there rules
Example : √8-√5 can also be written in a different way like √8-5, just like addition subtraction also can have a definite answer, it can't be written as √3 as the solution will be wrong
Simplifying Surds
If we take the √20, most of the people simplify it like √10 x √2, √1 x √20 or √4 x √5. There is a unique and a particular way of simplifying the surd, we take numbers that have a root like 4, the √4 results to 2 and the surd will be written as 2√5