# Typescript Numeric Literal Types How To Find Nth Root of X

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In this post we are going to try to find nth root of x

where x and n are both numeric literal types

to do this, we need to utilize exponentiation type with a slight modification:

type CreateArrayWithLengthX<

LENGTH extends number,

ACC extends unknown[] = [],

> = ACC['length'] extends LENGTH

? ACC

: CreateArrayWithLengthX<LENGTH, [...ACC,1]>type Multiplication<X extends number, Y extends number, Z extends number[] = [], V extends unknown[] = []> =

[...CreateArrayWithLengthX<Y>]['length'] extends Z['length']

? V

: Multiplication<X,Y,[1,...Z],[...CreateArrayWithLengthX<X>,...V]>

type Exponentiation<X extends number, N extends number, Counter extends number[] =[], Acc extends unknown[] = [1]> =

Counter['length'] extends N

? Acc // modified

: Exponentiation<X, N, [1, ...Counter], Multiplication<Acc['length'],X> >

ok, we have the building block now, let’s do it

type Root <X extends number, N extends number, Counter extends number[] = []> =

[...Exponentiation<Counter['length'], N>]['length'] extends X

? Counter['length']

: Root<X, N, [1,...Counter]>type A = Root<4,2> // 2

type B = Root<8,3> // 2

type C = Root<81,4> // 3

type D = Root<625,4> // 5

type E = Root<1024,10> // 2

type F = Root<2187,7> // 3

type G = Root<9261,3> // 21

limitation: X and N must be positive integers and only works with positive integer root. X cannot exceed 9,999 because the max tuple size is 9,999

X can exceed 999 if result^(N-1) is less than 1000

Warning, please insert the input one by one or else it will break the playground.