What is the number under the radical sign called?

The number under the radical sign is called the radicand. For example, in √16, the radicand is 16. The radical sign itself indicates a root, most often a square root.

Is the number under the square root sign called the radicand?

Yes, the number under the square root sign is called the radicand. In an expression like √25, 25 is the radicand, and the symbol √ is the radical sign. This term applies to any root, not just square roots.

What is the difference between a radicand and an index?

The radicand is the number underneath the radical sign, while the index is the small number outside the radical that tells you which root to take. For example, in ∛8, the index is 3 and the radicand is 8. If no index is written, it is understood to be 2, meaning a square root.

Can the radicand be negative?

The radicand can be negative for odd roots, such as ∛-8 = -2. However, for even roots like square roots, a negative radicand is not a real number. In those cases, the result is an imaginary number.

What does the radicand represent in a radical expression?

The radicand is the value you are taking the root of. It tells you what number or expression is being evaluated under the radical sign. For instance, in √(x + 1), the radicand is x + 1.

The Number Under the Radical Sign Is Called the Radicand

The number under the radical sign is called the radicand. In √49, the radicand is 49; in ∛8, it is 8; and in √(x + 3), it is the entire expression x + 3. The radicand is the value being rooted, while the radical sign (√) is the symbol telling you to take a root. Knowing the term matters because the radicand determines whether a radical is defined, how it simplifies, and what values are allowed.

Direct Answer

A radical expression places a radical sign (√) over a quantity. That quantity — everything beneath the horizontal bar — is the radicand, the name for the input of a root operation.

In √25, the radicand is 25. The symbol itself is not the radicand; it is the operator. The radical sign is the verb (“take the root”), and the radicand is the object (“this number”). The word comes from the Latin radix, meaning “root,” which is why the symbol and the number under it share a root word. Encyclopedia Britannica notes that radical expressions are defined by both the root being taken and the quantity beneath the sign — exactly the distinction the term “radicand” captures.

Radicand vs. Other Parts

Radicals have several moving parts, and beginners often blur them together. Separating them makes every later rule easier to follow.

The radical sign

The radical sign (√) indicates a root. When no small number appears in its “hook,” it means a square root.

The index

The index is the small number written in the notch of the radical sign. It tells you which root to take: an index of 3 means a cube root (∛), an index of 4 means a fourth root. When the index is 2, it is normally left unwritten. In ∛64, the index is 3 and the radicand is 64.

The coefficient

A coefficient is any number multiplying the radical from outside, as in 5√9. Here 5 is the coefficient and 9 is the radicand. The coefficient multiplies the result of the root — it is not part of the radicand, and mixing the two up is one of the most common errors in simplifying radicals.

Expression	Index	Radicand	Coefficient
√36	2 (implied)	36	none (1)
∛27	3	27	none (1)
4√16	2 (implied)	16	4
∜81	4	81	none (1)

Examples of Radicands

Identifying radicands becomes second nature with a few examples across square roots, cube roots, and variable expressions.

Square roots

√64 — the radicand is 64, and since 8 × 8 = 64, the value is 8.
√50 — the radicand is 50. It is not a perfect square, but it simplifies: √50 = √(25 × 5) = 5√5.

Cube roots and higher

∛125 — the radicand is 125. Because 5 × 5 × 5 = 125, the value is 5.
∛(-8) — the radicand is -8. Odd roots of negative numbers are defined, so the value is -2, since (-2)³ = -8.
∜16 — the radicand is 16, and the principal fourth root is 2.

Variable expressions

√(x²) — the radicand is x². For real numbers, √(x²) = |x|, the absolute value, not simply x.
√(9y²) — the radicand is the whole product 9y², which simplifies to 3|y|.
√(x + 7) — the radicand is the binomial x + 7. The entire expression under the bar counts, not just the x.

Whenever a radical covers a parenthetical or grouped expression, the group — not just the first symbol inside it — is the radicand.

Why the Radicand Matters

The radicand is not just a label. It controls two things you do with every radical: deciding whether the expression is defined, and simplifying or evaluating it.

Domain restrictions

In the real number system, an even-index radical requires a non-negative radicand. √(-9) has no real value, because no real number squared gives -9. That fact drives domain questions: for f(x) = √(x − 4), the radicand x − 4 must satisfy x − 4 ≥ 0, so the domain is x ≥ 4. Khan Academy covers this constraint as a core rule of radical functions, and it applies to every even root — square roots, fourth roots, and beyond. Odd roots accept any real radicand, positive or negative.

Simplifying and evaluating

The radicand also decides how much a radical can be simplified. Pulling out perfect-square (or perfect-cube) factors depends entirely on the radicand’s factorization. Compare:

√72 → radicand 72 = 36 × 2 → 6√2
√24 → radicand 24 = 4 × 6 → 2√6
√17 → radicand 17 is prime, so it stays as is

You can only extract a factor that appears enough times to match the index; everything else stays inside the radicand. Numerical values likewise come straight from the radicand: ∛64 = 4 because 4³ = 64.

A short worked example ties it together. Simplify √(48x²). The radicand is 48x². Factor it as 16 · 3 · x². Since 16 and x² are perfect squares, √(48x²) = 4x√3 if x is assumed non-negative, or 4|x|√3 in general. Every step was governed by what was inside the radicand — the sign outside never changed.

How the Radicand Behaves Under Operations

The radicand interacts with multiplication and division in ways that often surprise students.

Multiplication and division of roots

For non-negative radicands, √a · √b = √(ab). The radicands multiply, and a single radical results. So √3 · √12 = √36 = 6. Be careful with negatives: √(-4) · √(-9) is not √36, because neither factor is real to begin with. Division works the same way when the divisor’s radicand is positive: √50 / √2 = √25 = 5.

Addition and subtraction do not combine radicands

This is the most common trap. √9 + √16 = 3 + 4 = 7, not √25 = 5. Radicands can only be merged by addition or subtraction when the radicals are like terms — identical index and identical radicand — as in 2√7 + 5√7 = 7√7. If the radicands differ, nothing combines until you simplify each radical separately and check whether the radicands then match.

Key Takeaways

The number or expression under a radical sign is the radicand.
The radical sign is the root symbol itself; the index names which root (cube, fourth, etc.); the coefficient multiplies the radical from outside.
In √49 the radicand is 49; in ∛8 it is 8; in √(x + 3) it is the whole expression x + 3.
For even roots, a negative radicand is undefined in the real numbers, which creates domain restrictions; odd roots accept any real radicand.
Simplifying a radical depends on factoring the radicand to pull out perfect powers matching the index.

The Number Under the Radical Sign Is Called the Radicand: What Is It?