# Vocabulary/percentco

 %: 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.