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Like Radicals


Radicals are root expressions of any number like square root or cube root. They are very important in understanding square roots, cube roots.

Radicals which have same index and same radicand are called as like Radicals. They should be in simplest form, to check whether they are like or unlike. Radicals having same degree value are called as like expressions.

Some time, these expressions are not in their simplest form. So for calculation of these expressions, we need to simplify them to the lowest level. We cannot get one single number as end result, while adding or subtracting like radicals.

Example of Like radicals are : $\sqrt{2}, \sqrt{3}, \sqrt{5}, \sqrt{9}, ……..$

Components of Radical Expressions:

  1. Radicand: Number inside root sign. We find the root of that number.
  2. Degree: It tells us the number of times a radicand is multiplied by itself. Square root means radicand is multiplied 2 times.
Symbol: It is represented by $\sqrt{}$ and the length of this bar is very important in any expression. So, before solving any radical expression, check length of the bar. It can change the whole result. It is like brackets or parenthesis, which helps us in grouping and order of solving the expression

Binary operations are applied only on like radicals.

Operations like addition, subtraction are performed on radicals having same degrees. If radicals are unlike, we have to convert them to like radicals. It is same as adding or subtracting variable, where operation is performed on component.

Subtracting Like Radicals

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Subtracting like Radicals are very similar to adding Like Radicals.

One condition from the two must be applied in case of subtracting like radicals. Otherwise, we will call it unlike radicals. If radicals have same index, we can easily subtract the radicand value. There are two conditions under which we can subtract two radical values.

Condition 1: Radical values must contain an index value and a radical value. When radicand values are same and index values are different, then we can subtract two radicands.

Condition 2:
When we have two like radicals, but they are having same index and different radicands, we have to make the radicands equal to each other. And then, we perform subtraction operation.

Adding Like Radicals

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Radicals are numbers which are represented by radical sign. This radical sign is denoted by $\sqrt{}$. We use this radical sign, when we want to find roots of a number. Here, we will discuss adding like Radicals. For this we should know that radicals are of two types: like radicals and unlike Radicals. The number over radical sign is known as index of radical and number under radical sign is known as radicand.

In like radicals, radicands are always equal. If radicands are not equal, then it will be counted in unlike radicals. It is not necessary that index of radicals will be equal. Index can be different for different radicals.

Condition 1: When we have two like radicals with same index and we want to add these two radicals, then we follow a procedure as follows: First, we take two numbers say 'a' and 'b'. When we add these two radicals, we represent them as $\sqrt{a} + \sqrt{b}$. If 'a' and 'b' are equal, then we simply add these two radicals.
Condition 2: If index of two radicals are not equal and radicands are equal, then we add like radicals.
Condition 3: In this, index is same and the radicands are different. To add these two radicals, we make radicands equal.

Multiplying Like Radicals

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Multiplying like radicals in mathematics requires a technique that is different from other number types.

While multiplying radical expressions, we need to be aware of both values: one present inside the root symbol and one on the symbol.

Result of multiplication of like radicals will have same index as those of radicals and terms inside root sign are multiplied to give desired product. If radicals have coefficients also, they are multiplied separately to produce a new coefficient.