diff --git a/src/__test__/numbers.spec.js b/src/__test__/numbers.spec.js
index 95f3658..f1a8602 100644
--- a/src/__test__/numbers.spec.js
+++ b/src/__test__/numbers.spec.js
@@ -10,4 +10,9 @@ describe('the numbers-only bundle', () => {
       assert.strictEqual(math.isnan(-16.5), 0)
       assert.strictEqual(math.isnan(NaN), 1)
    })
+   it('takes sqrt with NaN for negative', () => {
+      assert.strictEqual(math.sqrt(25), 5)
+      assert(math.isnan(math.sqrt(-25)))
+      assert(math.isnan(math.sqrt(NaN)))
+   })
 })
diff --git a/src/number/__test__/arithmetic.spec.js b/src/number/__test__/arithmetic.spec.js
index 7d368cb..6d718ef 100644
--- a/src/number/__test__/arithmetic.spec.js
+++ b/src/number/__test__/arithmetic.spec.js
@@ -1,5 +1,6 @@
 import assert from 'assert'
 import math from '#nanomath'
+import {ReturnTyping} from '#core/Type.js'
 
 describe('number arithmetic', () => {
    it('supports basic operations', () => {
@@ -14,4 +15,18 @@ describe('number arithmetic', () => {
       assert.strictEqual(math.subtract(4, 2), 2)
       assert.strictEqual(math.quotient(7, 3), 2)
    })
+   it('takes square root of numbers appropriately', () => {
+      assert(isNaN(math.sqrt(NaN)))
+      assert.strictEqual(math.sqrt(4), 2)
+      assert.deepStrictEqual(math.sqrt(-4), math.complex(0, 2))
+      math.config.returnTyping = ReturnTyping.conservative
+      assert(isNaN(math.sqrt(NaN)))
+      assert.strictEqual(math.sqrt(4), 2)
+      assert(isNaN(math.sqrt(-4)))
+      math.config.returnTyping = ReturnTyping.full
+      assert(isNaN(math.sqrt(NaN)))
+      assert.deepStrictEqual(math.sqrt(4), math.complex(2, 0))
+      assert.deepStrictEqual(math.sqrt(-4), math.complex(0, 2))
+      math.config.returnTyping = ReturnTyping.free
+   })
 })
diff --git a/src/number/arithmetic.js b/src/number/arithmetic.js
index 662a157..0b5c66f 100644
--- a/src/number/arithmetic.js
+++ b/src/number/arithmetic.js
@@ -1,4 +1,10 @@
 import {plain} from './helpers.js'
+import {NumberT} from './NumberT.js'
+import {OneOf, Returns, ReturnTyping} from '#core/Type.js'
+import {match} from '#core/TypePatterns.js'
+import {Complex} from '#complex/Complex.js'
+
+const {conservative, full} = ReturnTyping
 
 export const abs = plain(Math.abs)
 export const absquare = plain(a => a*a)
@@ -18,5 +24,25 @@ export const cbrt = plain(a => {
 export const invert = plain(a => 1/a)
 export const multiply = plain((a, b) => a * b)
 export const negate = plain(a => -a)
+
+export const sqrt = match(NumberT, (math, _N, strategy) => {
+   if (!math.types.Complex || strategy === conservative) {
+      return Returns(NumberT, Math.sqrt)
+   }
+   const cplx = math.complex.resolve([NumberT, NumberT], full)
+   if (strategy === full) {
+      const cnan = math.nan(Complex(NumberT))
+      return Returns(Complex(NumberT), a => {
+         if (isNaN(a)) return cnan
+         return a >= 0 ? cplx(Math.sqrt(a), 0) : cplx(0, Math.sqrt(-a))
+      })
+   }
+   // strategy === free, return "best" type
+   return Returns(OneOf(NumberT, Complex(NumberT)), a => {
+      if (isNaN(a)) return NaN
+      return a >= 0 ? Math.sqrt(a) : cplx(0, Math.sqrt(-a))
+   })
+})
+
 export const subtract = plain((a, b) => a - b)
 export const quotient = plain((a,b) => Math.floor(a/b))
diff --git a/src/package.json b/src/package.json
index 290fb63..2e7d812 100644
--- a/src/package.json
+++ b/src/package.json
@@ -1,8 +1,9 @@
 {
     "imports" : {
         "#nanomath": "./nanomath.js",
-        "#boolean/*.js": "./boolean/*.js",
         "#core/*.js": "./core/*.js",
+        "#boolean/*.js": "./boolean/*.js",
+        "#complex/*.js": "./complex/*.js",
         "#generic/*.js": "./generic/*.js",
         "#number/*.js": "./number/*.js"
     },