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The number or expression written under a root symbol or radical sign is known as a radicand in math. It is an expression of which we are taking a root. For example, if we say that the cube root of 27 is 3. Here, 27 is the radicand.
|1.||What is a Radicand?|
|2.||Radical and Radicand|
|3.||Radicand and Index|
|4.||FAQs on Radicand|
What is a Radicand?
A radicand, in math, is an expression or any number or variable written inside a root symbol. It is the quantity of which we are finding the root. The term "radicand" is used when we learn about exponents and roots. So the value of radicand in √2 is 2. Some examples of radicand are given below:
3√(pq) → pq is the radicand
√(a+b) → a + b is the radicand
4√15 → 15 is the radicand
Radical and Radicand
A radical is a symbol used to denote the root of a number. It is represented as √. And the term or expression written below the radical sign is called the radicand. So, it can be said that radical is the symbol of the radicand. In other words, the radicand symbol is √.
There is one more term associated with the radicand which is called index. Let's learn about it.
Radicand and Index
Till now, you must have already understood the meaning of radicand. Now, if we observe the above examples carefully, you will find that there is a small number written on the top left of the radicand sign. Its value is generally a natural number greater than 1. For an instance, in 3√(pq), 3 is written on the top left of the radicand. This quantity is known as an index in math. In simple words, it is the value of the root. In case when there is no value of index mentioned on the left of the radicand symbol, we consider the value of the index as 2.
Topics Related to Radicand
Check these interesting articles related to the concept of radicand in math.
Example 1: Identify the radicand in the expression √53 + 24 - ab.
Solution: In the given expression √53 + 24 - ab, there is only one term written under the radical sign which is 53. Therefore, 53 is the radicand.
Example 2: Simplify the radicand in the given expression: √128 × √32.
Solution: According to the radicand rules, √x.√y = √xy. So, √128 × √32 = √(128×32) = √4096 = 64. Therefore, 64 is the required answer.
Example 3: Identify the values of radicand and index in the expression 8√122.
Solution: The given expression can be written as 8√144, as 122 = 144. The index is the number written on the top left of the radical sign. And radicand is the number or expression written under the root symbol. Therefore, 8 is the index and 144 or 122 is the radicand.
Practice Questions on Radicand
FAQs on Radicand
What is Radicand in Math?
The radicand in algebra is the term written under a radical sign or a root symbol. For example, if it is given that 10 is the square root of 100. Here, 100 is the radicand.
What is a Radical Index and Radicand?
There are three terms associated with the exponents and roots - radical, index, and radicand. Radical is the symbol of radicand, an index is a number written on the top left of the radical sign which denotes the order, and radicand is the term or the expression of which we are taking a root. For example, if it is given that the cube root of 64 is 4. We can write it as 3√64 = 4. Here, 64 is radicand, 3 is the index, and √ is the radical sign.
What is the Radicand in the Expression?
In an expression, radicand is the term(s) written under the root symbol. In the expression √64 - p + q - pq, the value of radicand is 64.
What if the Radicand is Negative?
If there is a negative radicand, it implies that its root is negative. The root of that number will be imaginary.
How to Multiply Radicals with the Same Radicand?
Multiplying radicals with the same radicand results in the value of radicand only (without root symbol). For example, √x × √x = x.
How to Simplify Radicals with Negative Radicand?
To simplify radicals with negative radicand, one should be familiar with the concept of complex numbers. We use iota (i) to remove the negative sign from the radicand. For example, √-81 can be written as i√81, where the value of iota is √-1.
How to Simplify a Radicand?
To simplify a radicand, we use the following radicand rules:
- n√x × n√y = n√(xy)
- n√x ÷ n√y = n√(x/y)
- n√xn = x
What is the Radicand in the Quadratic Formula?
Discriminant is the radicand in the quadratic formula. The quadratic formula of a quadratic equation ax2 + bx + c is x = [- b ± √(b2 - 4ac)]/2a. In this, the value written under the root sign is b2 - 4ac, which is discriminant.