How to Solve Surds?

TopA surd is a number which cannot be simplified and is written in the form of the Square root, cube root or the nth root of any number. Suppose we write a number say square root (4), its value will be 2, so it is not a surd. But if the number is written as square root (6), we know that it is not a perfect square root of any number, so it is a surd. We say that the Numbers which can be sometimes rational and sometimes irrational are called as surds. Let us now, learn how to solve surds. In order to learn how to solve surds, we will first find the factors of given roots and then make pairs of roots in order to get the result. Thus, we say that if we have the problem:
Square root (125 ) * square root ( 5 ) can be solved as follows :
125 = 5 * 5 * 5 and factors of 5 = 5, which is the prime number
So the given problem can be written as:
Square root (5 * 5 * 5 * 5),
= 5 * 5,
= 25.
Similarly, if we have the problem of addition or subtraction, it can be solved as follows: the numbers are written in the form of the same base and then operations are performed. Now we will take the following example and see how to solve:
Add root( 12 ) and root ( 27 )
We know factors of 12 are 2 * 2 * 3 and the factors of 27 are 3 * 3 * 3
So we can write root (12) as 2 * root (3 ) and root ( 27 ) can be written as 3 * root ( 3)
Thus we get = 2 root ( 3) + 3 root(3)
= 5 root ( 3).