Radicand: Definition & Concept

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  • 0:02 Radicals
  • 1:15 History of the Radicand
  • 1:42 Sample Problems
  • 2:24 Real-Life Examples
  • 3:29 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe

Jennifer has an MS in Chemistry and a BS in Biological Sciences.

A radicand is the number under a radical symbol (√). This lesson will describe the radicand in more detail and give some examples of problems involving radicands.


In mathematics, the term radical refers to an operation involving the radical symbol, which looks like this: √

When the operation involves the radical symbol with just a number inside, called the radicand, it is shorthand for square root. To solve these problems, take the square root of the radicand. The square root of a number is the number that, when multiplied by itself, or squared is equal to the radicand.

For example, √(25) is 5 because 5 x 5 = 25

If there is a subscript number in front of the radical symbol, that number tells you how many times a number should be multiplied by itself to equal the radicand. It's the opposite of an exponent, just like addition is the opposite of subtraction or division is the opposite of multiplication.

For example, 3√(8) = 2 because 23 = 8 or 2 x 2 x 2 = 8

and 5√(243) = 3 because 35 = 243 (3 x 3 x 3 x 3 x 3 = 243)

History of the Radicand

The terms 'radicand' and 'radical' are both derived from the Latin word 'radix,' which means 'root.' The reason for this is that the root is the source of something, like the root of a word. If you square or cube a number, the number that it came from is the root, while the number itself (the radicand) grows from that root. The first usage of these terms was seen in England in the mid-1600s in a book called An Introduction to Algebra by John Pell.

Sample Examples

Now, let's work through a few sample problems.

1. Which number is the radicand in the following expression?

4√(16) = 2

Remember, the radicand is the number inside the square root symbol, which, in this case, is 16.

2. Solve √(100)

From basic math facts, we know that 10 x 10 = 100, so the square root of 100 is 10.

3. Solve 3√(512)

This one takes a bit more work, but ultimately, we can determine that the cube root of 512 is 8 (8 x 8 x 8 = 512)

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