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# Lesson 6.5: Radicals

## Symbols

$\sqrt{\phantom{\rule{.5em}{0ex}}}\phantom{\rule{.3em}{0ex}}\text{open radical}$

$\text{close radical}$

$\surd \phantom{\rule{.3em}{0ex}}\text{radical sign without vinculum}$
⠐⠩

## Explanation

In mathematics, an expression containing the radical symbol is known as a radical expression. The radical symbol is used to write the most common radical expression the square root. The level of a square root, also known as the index, is two. It is not shown in print since it is the most common of the roots and it is understood to be two. The radical symbol is followed by the radicand (quantity from which the root is to be extracted) which is enclosed under the vinculum (horizontal bar). In braille, the radical expression must appear within the opening and closing radical symbols. The opening radical indicator is dots one four six and the closing radical indicator is dots three four six. Both have a grade 2 meaning and therefore they must be in grade 1 mode.

### Example 1

$\sqrt{16}$
⠰⠩⠼⠁⠋⠬

### Example 2

$-\sqrt{25}$
⠐⠤⠰⠩⠼⠃⠑⠬

### Example 3

$\sqrt{30+6}$
⠰⠩⠼⠉⠚⠐⠖⠼⠋⠬

The numeric indicator turns on grade 1 mode, so the grade 1 indicator is not needed before the radical indicator in Example 4.

### Example 4

$2\sqrt{25}$
⠼⠃⠩⠼⠃⠑⠬

### Example 5

$6\sqrt{2}-3\sqrt{5}$
⠼⠋⠩⠼⠃⠬⠐⠤⠼⠉⠩⠼⠑⠬

The radical sign without vinculum symbol does not need to be in grade 1 mode because the symbol does not have a grade 2 meaning.

### Example 6

$\text{Use the √ symbol.}$
⠠⠥⠎⠑⠀⠮⠀⠐⠩⠀⠎⠽⠍⠃⠕⠇⠲

### Example 7

$\sqrt{x+y}$
⠰⠩⠭⠐⠖⠽⠬

### Example 8

$\frac{7\sqrt{2}}{3\sqrt{2}}$
⠰⠷⠼⠛⠩⠼⠃⠬⠨⠌⠼⠉⠩⠼⠃⠬⠾

### Example 9

$\sqrt{\frac{8}{3}}$
⠰⠩⠼⠓⠌⠉⠬

When an expression includes multiple opening and closing symbols of any type, the symbols must be terminated in the reverse order in which they were opened.

### Example 10

$\sqrt{\frac{x}{8}}$
⠰⠰⠩⠷⠭⠨⠌⠼⠓⠾⠬

### Example 11

$\sqrt{{x}^{4}}$
⠰⠰⠩⠭⠔⠼⠙⠬