diff --git a/src/client/ClientGameRunner.ts b/src/client/ClientGameRunner.ts
index 555272e8e..1082b8bdb 100644
--- a/src/client/ClientGameRunner.ts
+++ b/src/client/ClientGameRunner.ts
@@ -11,8 +11,7 @@ import {
 import { createGameRecord } from "../core/Util";
 import { ServerConfig } from "../core/configuration/Config";
 import { getConfig } from "../core/configuration/ConfigLoader";
-import { TeamName, Unit, UnitType } from "../core/game/Game";
-import { TileRef } from "../core/game/GameMap";
+import { TeamName, UnitType } from "../core/game/Game";
 import {
   ErrorUpdate,
   GameUpdateType,
@@ -20,7 +19,7 @@ import {
   HashUpdate,
   WinUpdate,
 } from "../core/game/GameUpdates";
-import { GameView, PlayerView, UnitView } from "../core/game/GameView";
+import { GameView, PlayerView } from "../core/game/GameView";
 import { loadTerrainMap, TerrainMapData } from "../core/game/TerrainMapLoader";
 import { UserSettings } from "../core/game/UserSettings";
 import { WorkerClient } from "../core/worker/WorkerClient";
@@ -36,15 +35,6 @@ import {
 import { createCanvas } from "./Utils";
 import { createRenderer, GameRenderer } from "./graphics/GameRenderer";
 
-export // Is this function needed?
-function distSortUnitWorld(tile: TileRef, game: GameView) {
-  return (a: Unit | UnitView, b: Unit | UnitView) => {
-    return (
-      game.euclideanDist(tile, a.tile()) - game.euclideanDist(tile, b.tile())
-    );
-  };
-}
-
 export interface LobbyConfig {
   serverConfig: ServerConfig;
   flag: string;
diff --git a/src/core/execution/MIRVExecution.ts b/src/core/execution/MIRVExecution.ts
index 59d292527..bd0120c22 100644
--- a/src/core/execution/MIRVExecution.ts
+++ b/src/core/execution/MIRVExecution.ts
@@ -156,6 +156,7 @@ export class MirvExecution implements Execution {
 
   randomLand(ref: TileRef, taken: TileRef[]): TileRef | null {
     let tries = 0;
+    const mirvRange2 = this.mirvRange * this.mirvRange;
     while (tries < 100) {
       tries++;
       const x = this.random.nextInt(
@@ -174,7 +175,7 @@ export class MirvExecution implements Execution {
       if (!this.mg.isLand(tile)) {
         continue;
       }
-      if (this.mg.euclideanDist(tile, ref) > this.mirvRange) {
+      if (this.mg.euclideanDistSquared(tile, ref) > mirvRange2) {
         continue;
       }
       if (this.mg.owner(tile) != this.targetPlayer) {
diff --git a/src/core/execution/NukeExecution.ts b/src/core/execution/NukeExecution.ts
index 1ef305d22..913338e62 100644
--- a/src/core/execution/NukeExecution.ts
+++ b/src/core/execution/NukeExecution.ts
@@ -52,12 +52,11 @@ export class NukeExecution implements Execution {
   private tilesToDestroy(): Set<TileRef> {
     const magnitude = this.mg.config().nukeMagnitudes(this.nuke.type());
     const rand = new PseudoRandom(this.mg.ticks());
+    const inner2 = magnitude.inner * magnitude.inner;
+    const outer2 = magnitude.outer * magnitude.outer;
     return this.mg.bfs(this.dst, (_, n: TileRef) => {
-      const d = this.mg.euclideanDist(this.dst, n);
-      if (d > magnitude.outer) {
-        return false;
-      }
-      return d <= magnitude.inner || rand.chance(2);
+      const d2 = this.mg.euclideanDistSquared(this.dst, n);
+      return d2 <= outer2 && (d2 <= inner2 || rand.chance(2));
     });
   }
 
@@ -232,6 +231,7 @@ export class NukeExecution implements Execution {
       }
     }
 
+    const outer2 = magnitude.outer * magnitude.outer;
     for (const unit of this.mg.units()) {
       if (
         unit.type() != UnitType.AtomBomb &&
@@ -239,7 +239,7 @@ export class NukeExecution implements Execution {
         unit.type() != UnitType.MIRVWarhead &&
         unit.type() != UnitType.MIRV
       ) {
-        if (this.mg.euclideanDist(this.dst, unit.tile()) < magnitude.outer) {
+        if (this.mg.euclideanDistSquared(this.dst, unit.tile()) < outer2) {
           unit.delete();
         }
       }
diff --git a/src/core/game/GameImpl.ts b/src/core/game/GameImpl.ts
index bd13ceeac..b3ccc7eb9 100644
--- a/src/core/game/GameImpl.ts
+++ b/src/core/game/GameImpl.ts
@@ -684,8 +684,8 @@ export class GameImpl implements Game {
   manhattanDist(c1: TileRef, c2: TileRef): number {
     return this._map.manhattanDist(c1, c2);
   }
-  euclideanDist(c1: TileRef, c2: TileRef): number {
-    return this._map.euclideanDist(c1, c2);
+  euclideanDistSquared(c1: TileRef, c2: TileRef): number {
+    return this._map.euclideanDistSquared(c1, c2);
   }
   bfs(
     tile: TileRef,
diff --git a/src/core/game/GameMap.ts b/src/core/game/GameMap.ts
index e9392fe5f..65c6b5bae 100644
--- a/src/core/game/GameMap.ts
+++ b/src/core/game/GameMap.ts
@@ -38,7 +38,7 @@ export interface GameMap {
   forEachTile(fn: (tile: TileRef) => void): void;
 
   manhattanDist(c1: TileRef, c2: TileRef): number;
-  euclideanDist(c1: TileRef, c2: TileRef): number;
+  euclideanDistSquared(c1: TileRef, c2: TileRef): number;
   bfs(
     tile: TileRef,
     filter: (gm: GameMap, tile: TileRef) => boolean,
@@ -266,11 +266,10 @@ export class GameMapImpl implements GameMap {
       Math.abs(this.x(c1) - this.x(c2)) + Math.abs(this.y(c1) - this.y(c2))
     );
   }
-  euclideanDist(c1: TileRef, c2: TileRef): number {
-    return Math.sqrt(
-      Math.pow(this.x(c1) - this.x(c2), 2) +
-        Math.pow(this.y(c1) - this.y(c2), 2),
-    );
+  euclideanDistSquared(c1: TileRef, c2: TileRef): number {
+    const x = this.x(c1) - this.x(c2);
+    const y = this.y(c1) - this.y(c2);
+    return x * x + y * y;
   }
   bfs(
     tile: TileRef,
@@ -322,8 +321,10 @@ export function euclDistFN(
   dist: number,
   center: boolean = false,
 ): (gm: GameMap, tile: TileRef) => boolean {
+  const dist2 = dist * dist;
   if (!center) {
-    return (gm: GameMap, n: TileRef) => gm.euclideanDist(root, n) <= dist;
+    return (gm: GameMap, n: TileRef) =>
+      gm.euclideanDistSquared(root, n) <= dist2;
   } else {
     return (gm: GameMap, n: TileRef) => {
       // shifts the root tile’s coordinates by -0.5 so that its “center”
@@ -333,7 +334,7 @@ export function euclDistFN(
       const rootY = gm.y(root) - 0.5;
       const dx = gm.x(n) - rootX;
       const dy = gm.y(n) - rootY;
-      return Math.sqrt(dx * dx + dy * dy) <= dist;
+      return dx * dx + dy * dy <= dist2;
     };
   }
 }
diff --git a/src/core/game/GameView.ts b/src/core/game/GameView.ts
index 6bd58eb79..e5423010e 100644
--- a/src/core/game/GameView.ts
+++ b/src/core/game/GameView.ts
@@ -529,8 +529,8 @@ export class GameView implements GameMap {
   manhattanDist(c1: TileRef, c2: TileRef): number {
     return this._map.manhattanDist(c1, c2);
   }
-  euclideanDist(c1: TileRef, c2: TileRef): number {
-    return this._map.euclideanDist(c1, c2);
+  euclideanDistSquared(c1: TileRef, c2: TileRef): number {
+    return this._map.euclideanDistSquared(c1, c2);
   }
   bfs(
     tile: TileRef,