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.
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)
Radicals are used in many areas of life. One equation that relies heavily on the use of square roots is the Pythagorean theorem. The ability to find the length of any side of a right triangle when you know the lengths of the other two sides is necessary in the fields of engineering and architecture. Anything that resembles a parabola, such as the flight of a baseball or the path of a bullet shot from a gun, will require solving a square root to determine distance, trajectory or other necessary information.
Let's look at an example using the Pythagorean theorem. The Pythagorean theorem will work for any right triangle. Here, we're given the length of side a (5) and side b (7).
We can plug these numbers into the Pythagorean theorem (c2= a2 + b2) to come up with the equation, c2 = 52 + 72. So c2 = 25 + 49 or c = √(74), which is 8.6023.
The radicand is the number found inside a radical symbol, and it's the number you want to find the root of. It could be a square root, cube root or other root, which will be defined by the subscript found outside and just before the radical symbol. If there is no number present, it's understood that the problem is asking for the square root. Finding the root of the radicand is the opposite operation of squaring (or cubing, etc.) a number and is used extensively in engineering and other scientific fields.