---
title: "Radical Symbol in Elementary Algebra"
description: "Radical Symbol in Elementary Algebra shows square and higher roots, with the radicand underneath and the index showing which root you need."
canonical: "https://fiveable.me/elementary-algebra/key-terms/radical-symbol"
type: "key-term"
subject: "Elementary Algebra"
unit: "Unit 9"
---

# Radical Symbol in Elementary Algebra

## Definition

The radical symbol, √, shows a root in Elementary Algebra. It usually means square root, and with an index it can also show cube roots, fourth roots, and other higher roots.

## What It Is

The radical symbol is the sign you use to show a root in Elementary Algebra, usually a square root. If you see √49, you read it as the square root of 49, which is 7 because 7 × 7 = 49.

The number or expression under the radical is called the radicand. That part matters because the radicand is what you are trying to take the root of. In a problem like √20, the 20 is the radicand, and your job is often to simplify it if possible, not just evaluate it.

When the radical has a small number written at the upper left, that number is the index. The index tells you which root to take. A square root has an implied index of 2, so √x means the same thing as ²√x, while ³√x means cube root and ⁴√x means fourth root.

A lot of Elementary Algebra work with radicals is about rewriting them in a cleaner form. For example, √72 can be simplified because 72 has a perfect square factor: √72 = √(36·2) = 6√2. That move matters because radicals are often easier to compare, add, or subtract after simplification.

A common mistake is treating the radical sign like it can be dropped. It cannot. √5 and 5 are not the same thing, and √(a+b) does not split into √a + √b. The radical symbol only tells you where the root applies, so you have to pay attention to exactly what is inside the symbol.

## Why It Matters

The radical symbol shows up whenever Elementary Algebra asks you to work with roots, simplify expressions, or combine radicals. It is the visual cue that tells you whether you are dealing with a square root, cube root, or another root, and that changes the whole setup of the problem.

This matters most in simplifying and combining radical expressions. You cannot add √2 + √3 the way you add like terms, because the radicands are different. But you can combine 2√5 + 3√5 because the radicals match, just like 2x + 3x.

It also connects directly to factoring and perfect powers. If a radicand contains a perfect square or perfect cube, you can pull that factor out of the radical. That is why knowing the symbol helps you spot what can be simplified and what has to stay under the root.

In higher roots, the same symbol keeps the notation compact while the index shows the root type. That makes it easier to work with expressions in later algebra, especially when equations involve exponents and radicals together.

## Connections

### Radicand

The radicand is the expression inside the radical symbol. If you misread the radicand, you will simplify the wrong part of the problem. In √18, the 18 is what you factor, check for perfect squares, and rewrite if possible.

### Square Root

A square root is the most common use of the radical symbol in Elementary Algebra. The symbol √ usually means square root unless an index says otherwise. That is why √25 equals 5, because 5 squared gives 25.

### Higher Roots

Higher roots use the same radical symbol with an index, like cube root or fourth root. The symbol stays familiar, but the index changes the meaning. This is where you start connecting roots to exponents more directly.

### [Perfect Powers](/elementary-algebra/key-terms/perfect-powers)

Perfect powers are numbers that come from raising integers to whole-number exponents, like 36 or 64. They matter because they can be pulled out of radicals during simplification. Spotting a perfect square factor is usually the first step in rewriting a radical.

## On the AP Exam

A quiz item or problem set question will usually ask you to read, simplify, or combine expressions that use the radical symbol. You might be asked to simplify √50, identify the radicand in ³√x, or decide whether two radicals are like terms. The move is to read the symbol correctly first, then check whether the number under it has a perfect square or perfect cube factor.

If the radical is part of an expression, you may need to simplify before doing anything else. For example, 2√8 becomes 4√2 after simplifying √8. On word problems, the symbol can also show up when a side length or measurement is written as a root, so you need to interpret it as an exact value, not just a decimal approximation.

## Radical Symbol vs Exponent

Radical notation and exponent notation are related, but they are not the same symbol. An exponent tells you repeated multiplication, while a radical asks for the number that would produce the value when raised to that power. For example, 5² = 25 and √25 = 5.

## Key Takeaways

- The radical symbol, √, tells you to take a root, usually a square root unless an index says otherwise.
- The number or expression under the symbol is the radicand, and that is the part you simplify or evaluate.
- Higher roots use the same symbol with an index, like cube root or fourth root.
- You can only combine radicals when the radicands match after simplifying.
- Perfect squares and other perfect powers make radical simplification easier because they can be pulled outside the symbol.

## FAQs

### What is the radical symbol in Elementary Algebra?

The radical symbol, √, means root in Elementary Algebra. Most of the time it refers to a square root, but with an index it can also show cube roots, fourth roots, and other higher roots. The expression under it is called the radicand.

### What is the difference between a radical symbol and a radicand?

The radical symbol is the sign itself, like √. The radicand is what is inside the symbol, like the 18 in √18. If you are simplifying a radical, you work on the radicand, not on the symbol.

### Can you add radicals with different numbers under the symbol?

Not directly. √2 + √3 does not combine because the radicands are different. You can only add or subtract radicals when they are like radicals, meaning they have the same radicand after simplification.

### How do you simplify an expression with a radical symbol?

Look for a perfect square, cube, or other perfect power factor inside the radicand. Then pull that factor out of the radical. For example, √72 becomes 6√2 because 72 contains 36, which is a perfect square.

## Related Study Guides

- [9.7 Higher Roots](/elementary-algebra/unit-9/7-higher-roots/study-guide/JJCbhCiglq3e6s10)
- [9.3 Add and Subtract Square Roots](/elementary-algebra/unit-9/3-add-subtract-square-roots/study-guide/vjQnWmho76Qi5krr)

## About This Document

Canonical Fiveable pages are available as Markdown at the same path plus `.md`.

- [llms.txt](https://fiveable.me/llms.txt): index of Fiveable's sections and URL patterns
- [llms-full.txt](https://fiveable.me/llms-full.txt): complete subject and unit listing
- [MCP server](https://fiveable.me/mcp): call Fiveable as tools instead of fetching pages (`https://fiveable.me/api/mcp`)
- [MCP server for AP teachers](https://fiveable.me/mcp/teachers): a teacher's classes, assignments and AP-rubric grading (`https://fiveable.me/api/mcp/teacher`)

## Structured Data

```json
{"@context":"https://schema.org","@graph":[{"@type":"LearningResource","@id":"https://fiveable.me/elementary-algebra/key-terms/radical-symbol#resource","name":"Radical Symbol in Elementary Algebra","url":"https://fiveable.me/elementary-algebra/key-terms/radical-symbol","learningResourceType":"Concept explainer","educationalLevel":"AP® / High School","about":{"@id":"https://fiveable.me/elementary-algebra/key-terms/radical-symbol#term"},"audience":{"@type":"EducationalAudience","educationalRole":"student"},"dateModified":"2026-07-03T02:21:24.034Z","isPartOf":{"@type":"Collection","name":"Elementary Algebra Key Terms","url":"https://fiveable.me/elementary-algebra/key-terms"},"publisher":{"@type":"Organization","name":"Fiveable","url":"https://fiveable.me"}},{"@type":"DefinedTerm","@id":"https://fiveable.me/elementary-algebra/key-terms/radical-symbol#term","name":"Radical Symbol","description":"The radical symbol, √, shows a root in Elementary Algebra. It usually means square root, and with an index it can also show cube roots, fourth roots, and other higher roots.","url":"https://fiveable.me/elementary-algebra/key-terms/radical-symbol","inDefinedTermSet":{"@type":"DefinedTermSet","name":"Elementary Algebra Key Terms","url":"https://fiveable.me/elementary-algebra/key-terms"}},{"@type":"FAQPage","mainEntity":[{"@type":"Question","name":"What is the radical symbol in Elementary Algebra?","acceptedAnswer":{"@type":"Answer","text":"The radical symbol, √, means root in Elementary Algebra. Most of the time it refers to a square root, but with an index it can also show cube roots, fourth roots, and other higher roots. The expression under it is called the radicand."}},{"@type":"Question","name":"What is the difference between a radical symbol and a radicand?","acceptedAnswer":{"@type":"Answer","text":"The radical symbol is the sign itself, like √. The radicand is what is inside the symbol, like the 18 in √18. If you are simplifying a radical, you work on the radicand, not on the symbol."}},{"@type":"Question","name":"Can you add radicals with different numbers under the symbol?","acceptedAnswer":{"@type":"Answer","text":"Not directly. √2 + √3 does not combine because the radicands are different. You can only add or subtract radicals when they are like radicals, meaning they have the same radicand after simplification."}},{"@type":"Question","name":"How do you simplify an expression with a radical symbol?","acceptedAnswer":{"@type":"Answer","text":"Look for a perfect square, cube, or other perfect power factor inside the radicand. Then pull that factor out of the radical. For example, √72 becomes 6√2 because 72 contains 36, which is a perfect square."}}]},{"@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Elementary Algebra","item":"https://fiveable.me/elementary-algebra"},{"@type":"ListItem","position":2,"name":"Key Terms","item":"https://fiveable.me/elementary-algebra/key-terms"},{"@type":"ListItem","position":3,"name":"Unit 9","item":"https://fiveable.me/elementary-algebra/unit-9"},{"@type":"ListItem","position":4,"name":"Radical Symbol"}]}]}
```