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Unlike Radicals

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In mathematics Radicals are denoted by a symbol '√' which is put over a number. This number is called radicand. Radicals can be of two types. One is like radical and other is unlike radical. This expression is used to denote the root sign of a number. When no sign is present before a radical then it is considered as positive radical. When we find Square root of number then radicand can have both signs i.e. positive and negative.
We can use radical sign to represent higher root than 2 such as Cube i.e. 3√x. We use here index number. This index number is put over the radical sign. If the index number is 'n' then radicand will have 'n' number of different roots.
Now we know that number over radical sign is called as index and number under the radical sign is called as radicand. The whole expression is called as radical expression.
Now we see unlike radicals’ definition which is given below:
Unlike radicals are radicals that do not have same index value. If we have two different Numbers and they do not have same index number then they are considered as unlike radicals.
Unlike radicals have two properties:
Property 1: If we have two radical numbers say 'x' and 'y', when 'x' and 'y' are radicands and they have different index over the radical sign then they will behave as the unlike radical number. If radicands are equal and index is also equal then they will be counted in Like Radicals.
Property 2: If two radical numbers have radicands as 'x' and 'y', when 'x' and 'y' have same index and x = y then they will be like radicals. If 'x' is not equals to 'y' then they will be unlike radicals.

Adding Unlike Radicals

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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

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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.

Subtracting Unlike Radicals

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We know that the Radicals are used in finding the Square root of a given number. If we know how to do addition and subtraction of Like Radicals then it will be easier to learn process of subtracting Unlike Radicals.
Radicals are represented by the sign '√'. This sign is used to differentiate the index and radicands of a radical. An index of radical is a number which is used to denote the order of root of that number; this is the number over radical sign. The radicand is a number whose square root we find; this is the number which is under radical sign.
Now we will see how we can subtract unlike radicals:
Unlike radicals are the radicals which differ in their index or radicands. In order to perform the operations such as addition, multiplication, subtraction we need to convert the unlike radicals into like radicals. Then only we can perform such operations.
If two radical Numbers have different radicands then they are unlike radicands. To understand the subtraction of unlike radicands let us take an example, this will help us to better understand it. We have two numbers as √98 and √8. We want to subtract √8 from the √98. But they are different in radicals so they are unlike radicals. Now we have to convert them in like radicals. For this we make radicands equal. We find the factors of both values 8 and 98. Now we get factors in radicals as √2 * 2 * 2 and √7 * 7 * 2 we take out common factors and we get 2√2 and 7√2 values. They are equal in their radicand value so we can subtract them easily. We get subtracted value as 5√2.