Surd is a Latin word that means mute or deaf. In the past, Arabian mathematicians referred to rational & irrational numbers as audible & inaudible, respectively. Because surds are formed up of irrational numbers, they were given the Arabic name asamm (deaf, stupid), which was ultimately translated into Latin as surds.
Surds are the square roots of non-trivial numbers. It is impossible to convey accurately in a fraction. In another way, Surd is an irrational root of the whole number. Consider the number √2 ≈1.414213. If we keep it as a surd √2, it will be more correct.
It’s important to keep in mind that an irrational number cannot be stated as a fraction.
Surds are square root values that cannot be easily converted to whole numbers or integers in mathematics.
Division of Surds
You can divide surds with various numbers inside the root by combining them into single root & dividing the numbers within the root as long as the indexes of roots are the same.
√a /√b = √a/ b
√14 / √2 = √14/2= √7
You can multiply surds with various numbers inside the root by combining them into single root & multiplying the numbers within the root as long as the indexes of roots are the same. Factors can also be used to divide a root into many roots.
√a ×√b= √a ×b
Example: √3 ×√5= √3 ×5= √15
You should get the original value if you multiply the square root of an integer by itself.
√a ×√a= √a ×a= √a²=a
Example: √5 ×√5= √5 ×5= √5²=5
Each term in the 1st bracket should be multiplied by each term in the 2nd bracket in order to multiply brackets containing surds. You can then mix phrases that are similar.
(2+ √3)+(5+√3)=2×5+2√3+5 √3+√3²
The order of the elements does not matter when multiplying a number by a surd, & the result must be the number followed by surd.
x × √y=√yx=x√y
Example: 3 ×√5=√5×3=3√5
The number within the roots should be the same to add or subtract surds. Outside the root, you add and subtract numbers.
Examples: 5 √3+3√3=(5+3)√3=8√3
Surds are expressions which result in an irrational number having infinite decimals when they have a Square Root, Cube Root, or other root. They’ve been left in their original state to better portray them.
The index of roots should be the same to multiply & divide surds with various numbers inside the root.
The number within the roots have to be the same while adding or subtracting surds.
It may be important to simplify surds before subtracting or adding them.
If a square number is a factor in the number within the root of a surd, it can be simplified.
There are following types of surds which are given here;