# Vocabulary/percentco

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`%: y`Square Root

Rank 0 *-- operates on individual atoms of y, producing a result of the same shape --*
WHY IS THIS IMPORTANT?

The *square root* of `y` .

%: 49 7

### Common Uses

Can lead to neater tacit expressions than using (`y^0.5`).

### Related Primitives

Double (`+: y`),
Square (`*: y`),
Halve (`-: y`)

`x %: y`Root

Rank 0 0 *-- operates on individual atoms of x and y, producing a result of the same shape --*
WHY IS THIS IMPORTANT?

The `x`*-th root* of `y` .

2 %: 49 NB. square-root 7 3 %: 49 NB. cube-root 3.65931

### Common Uses

Can lead to neater tacit expressions than using (`y^%x`).

### Details

1. `%: y` and `x %: y` return the *principal value* of the root, which is defined as ` ^ (^. y) % x`

The logarithm (`^.`) is in turn defined to use the angle in the range: (-π, π]

A consequence of this definition is that all roots of negative numbers are complex, even cube roots:

3 %: _1 0.5j0.866025

2. Taking an integer root of an extended integer by an integer (extended or not) produces an extended integer if the quotient is an integer, or floating-point otherwise.