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.
Adding Unlike RadicalsBack to Top
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 RadicalsBack to Top
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 RadicalsBack to Top
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.