# Lesson 6.6: More Radicals

## Review

In braille, the level change up indicator is used to identify the item that follows as being in the superscript position. The extent of the level change up indicator is the next item. Braille grouping indicators must be used to enclose an expression that includes more than one item.

## Explanation

In a cube or higher level radical, the radical index is printed as a smaller number above and to the left of the radical sign, in the crook of the radical. This index is placed in braille as a superscript expression immediately following the opening radical symbol.

### Example 1

$\sqrt[3]{27}$

⠰⠰⠩⠔⠼⠉⠼⠃⠛⠬

### Example 2

$\sqrt[m]{27}=3$

⠰⠰⠩⠔⠍⠼⠃⠛⠬⠀⠐⠶⠀⠼⠉

### Example 3

$\sqrt[m+n]{27}$

⠰⠰⠩⠔⠣⠍⠐⠖⠝⠜⠼⠃⠛⠬

### Example 4

$4+\sqrt[3]{27}$

⠼⠙⠐⠖⠩⠔⠼⠉⠼⠃⠛⠬

### Example 5

$5\sqrt[3]{27}$

⠼⠑⠩⠔⠼⠉⠼⠃⠛⠬

### Example 6

$\sqrt[3]{\frac{1}{8}}$

⠰⠰⠩⠔⠼⠉⠼⠁⠌⠓⠬

A nested radical is composed of two or more radicals where one or more is embedded in another. When the symbols are nested in braille, they must be closed or terminated in the reverse order in which they were opened. It is essential to identify which numerals appear under the radical sign in the nested expression.

### Example 7

$\sqrt{\sqrt{27}+6}$

⠰⠰⠩⠩⠼⠃⠛⠬⠐⠖⠼⠋⠬

### Example 8

$\sqrt{5-2\sqrt{5}}$

⠰⠩⠼⠑⠐⠤⠼⠃⠩⠼⠑⠬⠬

### Example 9

$\sqrt{\sqrt[3]{8000}}$

⠰⠰⠩⠩⠔⠼⠉⠼⠓⠚⠚⠚⠬⠬