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An expression that contains root values, such as Square roots, cube roots are known as Radicals. For example: √ (p + q), and 3√ (p + q). The value 2 means square root, 3 means Cube root and so on. Radicals are represented by the symbol '√'. Here we will discuss process of Adding Unlike Radicals.
Unlike radical means two radicals do not have same value. Now we will see procedure to add two or more unlike radicals.
Step 1: First we take two unlike radicals. Like √ 4 + 5√ 4.
Step 2: In the given expression find the common term if present.
= √ 4 + 5√ 4, In this number '1' and '5' are common in both the term. So put like term together.
So we can write the expression as:
= (1 + 5) √ 4;
Step 3: Now we can easily add radicals. So after adding we get:
= 6√ 4.
Suppose we have another expression 2 √6 + 4 √8 + √6 + 5 √8, Now we have to add radical values given in the expression.
Here also we have to apply the same above procedure to add radicals.
In this expression two pairs are same. So we can write them as:
= 2 √6 + 4 √8 + √6 + 5 √8;
= 2 √6 + √6 + 4 √8 + 5 √8,
Now find common term in expression.
= (2 + 1) √6 + (4 + 5) √8, now we can easily add the radicals.
On adding we get.
= 3 √6 + 9 √8. This is how we can add unlike radicals.

## Multiplying Unlike Radicals

Radicals are used to get Square root of a number. It is very simple to learn multiplying unlike Radicals. In order to learn multiplication of Unlike Radicals let us understand the radicals first. Radical may be Like Radicals or unlike radicals.
We represent radicals by the sign '√'. This sign is used to denote radical of a number. The number which is over radical sign is index of radical and number which is under radical sign is called radicand. We can get square root of both positive and negative number.
Now let us understand the multiplication of radicals: Multiplication of unlike radicals is same as multiplication of like radicals. If two radicals are different in their radicands then they are called unlike radicals. And when two radicals are different in their index value then also we call them unlike radicals.
In order to multiply unlike radicals, we need to convert unlike radicals in like radical. For this we make radicands of two radical Numbers equal by Factorization.
If radicals have same index values then we multiply radicands only in radical numbers and index remains the same. Let us understand with an example; if we want to multiply √4 and √2 then we get the answer by simply multiplying the radicands as √8.
If we have two radicals with different index and different radicand then this is an unlike radical. Now we multiply index with index and radicand with radicand. Just take an example as we want to multiply 3√2 and √2 now we get the multiplied value as 3√4 which is equals to the value 3 * 2 = 6.