Kalkulator Akar Pangkat Tiga
Temukan ∛x untuk bilangan apapun, termasuk negatif
Masukkan bilangan positif atau negatif untuk menghitung akar pangkat tiganya.
∛
Akar Pangkat Tiga Kalkulator
Hitung akar pangkat tiga dari bilangan positif maupun negatif secara instan. Dapatkan desimal presisi, bentuk sederhana, dan langkah kerja lengkap. 100% gratis.
Instan Langkah demi langkah 100% Gratis
Hitung Cepat — Akar Kubik Klik angka untuk mendapatkan hasil instan
Instant ∛ Calculation Simplified Radical Form Step-by-Step Breakdown 100% Free & Unlimited
Daftar Isi 16 Bagian Tampilkan Sembunyikan
Panduan Lengkap
Apa itu Akar Pangkat Tiga (Racine Cubique)?
Akar pangkat tiga adalah operasi penting dalam geometri 3 dimensi. Kalkulator kami memberikan jawaban akurat seketika.
Akar pangkat tiga adalah bilangan yang jika dikalikan dengan dirinya sendiri sebanyak 3 kali menghasilkan bilangan mula-mula (3 × 3 × 3 = 27, maka ∛27 = 3).
Radical Anatomy Explorer Click or hover over any part
³ √ 27 = 3
Index (Degree 3)
The small number 3 in the upper-left of the radical sign. It indicates you are finding the 3rd root (cube root) rather than a square root (index 2).
Radical Symbol
The mathematical sign ∛ denoting the extraction of the cube root. In Unicode, it is character U+221B.
Radicand
The number underneath the radical sign whose cube root is being calculated. It can be positive, negative, or zero.
Cube Root (Result)
The real value that, when multiplied by itself three times (y × y × y), equals the radicand.
∛8 = 2 karena 2 × 2 × 2 = 8
∛64 = 4 karena 4 × 4 × 4 = 64
∛1000 = 10 karena 10 × 10 × 10 = 1.000
Ini adalah dasar matematis untuk mencari rusuk kubus dari volumenya.
Petunjuk
Cara Menggunakan Kalkulator Akar Pangkat Tiga
Tiga langkah praktis:
1
Ketikkan Angka
Masukkan angka pada kolom di atas.
2
Klik Hitung
Tekan tombol untuk memproses.
3
Lihat Hasilnya
Dapatkan nilai desimal dan bentuk sederhana, termasuk angka negatif.
Alat ini menghitung seluruh tahapan tanpa perlu rumus rumit.
Notasi
Notasi Matematika: Simbol ∛
Simbol ∛ menandakan akar kubik dengan indeks angka 3.
∛64 = 4
Standard mathematical radical notation using index 3 and radical sign.
64^(1/3) = 4
Fractional power representation: raising any number to 1/3 equals its cube root.
Math.cbrt(64) // 4
Standard in JavaScript, Python (64 ** (1/3)), C, Java, and modern runtimes.
=POWER(A1, 1/3)
Excel and Google Sheets formula. Alternatively use =A1^(1/3).
\sqrt[3]64
LaTeX mathematical typesetting command for academic papers and documents.
Unicode: U+221B | HTML: ∛ | 221B + Alt+X
On Windows: type 221B then press Alt+X. On Mac: Cmd+Ctrl+Space. HTML: ∛.
Dapat juga dinyatakan sebagai pangkat pecahan:
x^(1/3) = ∛x
Kedua bentuk bernilai sama. Pada pemrograman dipakai x^(1/3).
Baik ∛x maupun x^(1/3) merujuk pada operasi yang sama.
Rumus
Definisi Akar Pangkat Tiga
Akar kubik didefinisikan sebagai kebalikan dari perpangkatan tiga:
If y = ∛x, then y × y × y = x (or y³ = x)
Dikalikan tiga kali berturut-turut, hasilnya harus kembali ke angka semula.
Sifat Dasar
Lima Sifat Akar Pangkat Tiga
Sifat operasi akar pangkat 3:
1
Sifat Perkalian
Memisahkan faktor radikan
∛8 × ∛27 = 2 × 3 = 6 = ∛216
Menyederhanakan angka kubik besar.
2
Sifat Pembagian
Memisahkan pembilang dan penyebut
∛64 ÷ ∛8 = 4 ÷ 2 = 2 = ∛8
Penarikan akar pecahan secara terpisah.
3
Sifat Perpangkatan
Pangkat tiga dan akar kubik saling meniadakan
∛(5³) = 5 dan ∛((-3)³) = -3
Berlaku untuk semua bilangan riil, positif maupun negatif!
4
Pemangkatan Tiga
Akar dipangkatkan 3 menghasilkan radikan
(∛5)³ = 5
Penting dalam penyelesaian persamaan aljabar.
5
Nilai Tetap
Akar dari 0 dan 1 selalu konstan
∛1 = 1 dan ∛0 = 0
Titik acuan matematis.
Working with higher degree root indices beyond 3? Compute 4th, 5th, and general nth roots online →
Metode
Cara Menghitung Akar Pangkat Tiga
Empat metode umum:
Method 1
1. Kalkulator Online (Paling Cepat)
Ketik angka dan dapatkan jawaban tepat seketika.
Method 2
2. Faktorisasi Prima
Kelompokkan faktor prima dalam kelompok 3.
Contoh: Menghitung ∛216
- 216 = 2³ × 3³
- Kelompok: (2×2×2) × (3×3×3)
- Akar: 2 × 3 = 6
Extended Example: Find ∛3375
- Decompose into prime factors: 3375 = 3 × 3 × 3 × 5 × 5 × 5
- Group into sets of three: (3 × 3 × 3) × (5 × 5 × 5) = 3³ × 5³
- Take one factor from each group: 3 × 5 = 15
- Therefore, ∛3375 = 15.
Method 3
4. Estimasi Interval
Tempatkan di antara dua kubik terdekat.
Contoh: Estimasi ∛50
- 3³ = 27
- 4³ = 64
- ∛50 berada di antara 3 dan 4 (sekitar 3,68).
Kubik Sempurna
Daftar Kubik Sempurna yang Perlu Dihafal
Kubik membesar dengan cepat. Inilah 10 yang pertama:
1³ = 1
∛1 = 1
2³ = 8
∛8 = 2
3³ = 27
∛27 = 3
4³ = 64
∛64 = 4
5³ = 125
∛125 = 5
6³ = 216
∛216 = 6
7³ = 343
∛343 = 7
8³ = 512
∛512 = 8
9³ = 729
∛729 = 9
10³ = 1,000
∛1,000 = 10
11³ = 1,331
∛1,331 = 11
12³ = 1,728
∛1,728 = 12
Gulir untuk melihat tabel ↓
| Number (n) | Cube (n³) | Cube Root (∛n³) | Quick Test |
|---|---|---|---|
| 1 | 1 | 1 | |
| 2 | 8 | 2 | |
| 3 | 27 | 3 | |
| 4 | 64 | 4 | |
| 5 | 125 | 5 | |
| 6 | 216 | 6 | |
| 7 | 343 | 7 | |
| 8 | 512 | 8 | |
| 9 | 729 | 9 | |
| 10 | 1,000 | 10 | |
| 11 | 1,331 | 11 | |
| 12 | 1,728 | 12 | |
| 15 | 3,375 | 15 | |
| 20 | 8,000 | 20 | |
| 25 | 15,625 | 25 | |
| 50 | 125,000 | 50 | |
| 100 | 1,000,000 | 100 |
Bilangan Negatif
Akar Bilangan Negatif (Nilainya Riil!)
Perbedaan terbesar dengan akar kuadrat: akar pangkat tiga bilangan negatif adalah bilangan riil biasa.
Hasil kali 3 angka negatif adalah negatif: negatif × negatif = positif, positif × negatif = negatif.
Square Root (Index 2)
√(-16) = No Real Root
Requires the imaginary unit i (±4i) because squaring any real number produces a non-negative result.
Cube Root (Index 3)
∛(-64) = -4
100% Real solution! Multiplying three negative numbers gives a negative product: (-4) × (-4) × (-4) = -64.
Contoh: ∛(−64)
∛(−64) = −4, karena (−4) × (−4) × (−4) = −64
∛(-x) = -∛x
Tidak memerlukan bilangan imajiner i: hasilnya 100% riil.
Beda Penting dengan Akar Kuadrat
Akar kuadrat negatif memerlukan satuan imajiner i, sedangkan akar pangkat tiga menghasilkan bilangan riil secara langsung.
Cube Root of Decimals & Cube Root of Fractions
Cube Root of Decimals & Cube Root of Fractions
Cube Root of Decimals
To find the cube root of a decimal, convert it into a fraction or power of ten, simplify, and evaluate the root.
Example: ∛0.008
- 0.008 = 8 / 1000 = 8 × 10⁻³
- ∛(8 / 1000) = ∛8 / ∛1000 = 2 / 10
- 2 / 10 = 0.2
Cube Root of Fractions
Apply the quotient property by taking the cube root of the numerator and denominator separately: ∛(a/b) = ∛a / ∛b.
Example: ∛(8 / 27)
- Apply quotient rule: ∛(8 / 27) = ∛8 / ∛27
- Evaluate numerator: ∛8 = 2
- Evaluate denominator: ∛27 = 3
- Result: 2 / 3 ≈ 0.6667
Penyederhanaan
Tabel Penyederhanaan Akar Pangkat Tiga
Keluarkan faktor kubik sempurna dari dalam akar:
| Bentuk Asal | Bentuk Sederhana | Alasan | Actions |
|---|---|---|---|
| ∛16 | 2∛2 | 16 = 2³ × 2 = 8 × 2 | |
| ∛24 | 2∛3 | 24 = 2³ × 3 = 8 × 3 | |
| ∛32 | 2∛4 | 32 = 2³ × 4 = 8 × 4 | |
| ∛40 | 2∛5 | 40 = 2³ × 5 = 8 × 5 | |
| ∛48 | 2∛6 | 48 = 2³ × 6 = 8 × 6 | |
| ∛54 | 3∛2 | 54 = 3³ × 2 = 27 × 2 | |
| ∛56 | 2∛7 | 56 = 2³ × 7 = 8 × 7 | |
| ∛72 | 2∛9 | 72 = 2³ × 9 = 8 × 9 | |
| ∛108 | 3∛4 | 108 = 3³ × 4 = 27 × 4 | |
| ∛128 | 4∛2 | 128 = 4³ × 2 = 64 × 2 | |
Cari bilangan kubik sempurna terbesar yang membagi radikan.
Perbandingan
Perbedaan Akar Kubik dan Akar Kuadrat
Perbandingan 3D vs 2D:
| Property / Feature | Akar Pangkat Tiga | Akar Kuadrat |
|---|---|---|
| Simbol | ∛ (Index 3) | √ (Index 2) |
| Exponent Form | x^(1/3) | x^(1/2) |
| Angka negatif | Hasil riil ada (∛-64 = -4) | Tidak ada hasil riil (butuh i) |
| Perkalian | 3 (x × x × x) | 2 (x × x) |
| Number of Real Roots | Exactly 1 for all real numbers | 1 for positive / 0 for negative |
| Graph Symmetry | Odd function (symmetric about origin) | Defined only for x ≥ 0 |
| Output Sign | Always matches input sign (∛(-8) = -2) | Always non-negative (principal root) |
| Contoh | ∛64 = 4 (4³=64) | √64 = 8 (8²=64) |
Need to evaluate square roots instead? Calculate square roots with exact decimals and simplified radicals →
Tabel Referensi
Tabel Lengkap Akar Kubik 1 sampai 100
Daftar nilai hingga 3 desimal dengan tanda kubik sempurna.
Gulir untuk melihat ke-100 nilai ↓
| Angka (n) | Akar (∛n) | Simplified Radical | Tipe | Quick Test |
|---|---|---|---|---|
| 1 | 1 | 1 | Kubik Sempurna | |
| 2 | 1.2599 | ∛2 | Irasional | |
| 3 | 1.4422 | ∛3 | Irasional | |
| 4 | 1.5874 | ∛4 | Irasional | |
| 5 | 1.7100 | ∛5 | Irasional | |
| 6 | 1.8171 | ∛6 | Irasional | |
| 7 | 1.9129 | ∛7 | Irasional | |
| 8 | 2 | 2 | Kubik Sempurna | |
| 9 | 2.0801 | ∛9 | Irasional | |
| 10 | 2.1544 | ∛10 | Irasional | |
| 11 | 2.2240 | ∛11 | Irasional | |
| 12 | 2.2894 | ∛12 | Irasional | |
| 13 | 2.3513 | ∛13 | Irasional | |
| 14 | 2.4101 | ∛14 | Irasional | |
| 15 | 2.4662 | ∛15 | Irasional | |
| 16 | 2.5198 | 2∛2 | Irasional | |
| 17 | 2.5713 | ∛17 | Irasional | |
| 18 | 2.6207 | ∛18 | Irasional | |
| 19 | 2.6684 | ∛19 | Irasional | |
| 20 | 2.7144 | ∛20 | Irasional | |
| 21 | 2.7589 | ∛21 | Irasional | |
| 22 | 2.8020 | ∛22 | Irasional | |
| 23 | 2.8439 | ∛23 | Irasional | |
| 24 | 2.8845 | 2∛3 | Irasional | |
| 25 | 2.9240 | ∛25 | Irasional | |
| 26 | 2.9625 | ∛26 | Irasional | |
| 27 | 3 | 3 | Kubik Sempurna | |
| 28 | 3.0366 | ∛28 | Irasional | |
| 29 | 3.0723 | ∛29 | Irasional | |
| 30 | 3.1072 | ∛30 | Irasional | |
| 31 | 3.1414 | ∛31 | Irasional | |
| 32 | 3.1748 | 2∛4 | Irasional | |
| 33 | 3.2075 | ∛33 | Irasional | |
| 34 | 3.2396 | ∛34 | Irasional | |
| 35 | 3.2711 | ∛35 | Irasional | |
| 36 | 3.3019 | ∛36 | Irasional | |
| 37 | 3.3322 | ∛37 | Irasional | |
| 38 | 3.3620 | ∛38 | Irasional | |
| 39 | 3.3912 | ∛39 | Irasional | |
| 40 | 3.4200 | 2∛5 | Irasional | |
| 41 | 3.4482 | ∛41 | Irasional | |
| 42 | 3.4760 | ∛42 | Irasional | |
| 43 | 3.5034 | ∛43 | Irasional | |
| 44 | 3.5303 | ∛44 | Irasional | |
| 45 | 3.5569 | ∛45 | Irasional | |
| 46 | 3.5830 | ∛46 | Irasional | |
| 47 | 3.6088 | ∛47 | Irasional | |
| 48 | 3.6342 | 2∛6 | Irasional | |
| 49 | 3.6593 | ∛49 | Irasional | |
| 50 | 3.6840 | ∛50 | Irasional | |
| 51 | 3.7084 | ∛51 | Irasional | |
| 52 | 3.7325 | ∛52 | Irasional | |
| 53 | 3.7563 | ∛53 | Irasional | |
| 54 | 3.7798 | 3∛2 | Irasional | |
| 55 | 3.8030 | ∛55 | Irasional | |
| 56 | 3.8259 | 2∛7 | Irasional | |
| 57 | 3.8485 | ∛57 | Irasional | |
| 58 | 3.8709 | ∛58 | Irasional | |
| 59 | 3.8930 | ∛59 | Irasional | |
| 60 | 3.9149 | ∛60 | Irasional | |
| 61 | 3.9365 | ∛61 | Irasional | |
| 62 | 3.9579 | ∛62 | Irasional | |
| 63 | 3.9791 | ∛63 | Irasional | |
| 64 | 4 | 4 | Kubik Sempurna | |
| 65 | 4.0207 | ∛65 | Irasional | |
| 66 | 4.0412 | ∛66 | Irasional | |
| 67 | 4.0615 | ∛67 | Irasional | |
| 68 | 4.0817 | ∛68 | Irasional | |
| 69 | 4.1016 | ∛69 | Irasional | |
| 70 | 4.1213 | ∛70 | Irasional | |
| 71 | 4.1408 | ∛71 | Irasional | |
| 72 | 4.1602 | 2∛9 | Irasional | |
| 73 | 4.1793 | ∛73 | Irasional | |
| 74 | 4.1983 | ∛74 | Irasional | |
| 75 | 4.2172 | ∛75 | Irasional | |
| 76 | 4.2358 | ∛76 | Irasional | |
| 77 | 4.2543 | ∛77 | Irasional | |
| 78 | 4.2727 | ∛78 | Irasional | |
| 79 | 4.2908 | ∛79 | Irasional | |
| 80 | 4.3089 | 2∛10 | Irasional | |
| 81 | 4.3267 | 3∛3 | Irasional | |
| 82 | 4.3445 | ∛82 | Irasional | |
| 83 | 4.3621 | ∛83 | Irasional | |
| 84 | 4.3795 | ∛84 | Irasional | |
| 85 | 4.3968 | ∛85 | Irasional | |
| 86 | 4.4140 | ∛86 | Irasional | |
| 87 | 4.4310 | ∛87 | Irasional | |
| 88 | 4.4480 | 2∛11 | Irasional | |
| 89 | 4.4647 | ∛89 | Irasional | |
| 90 | 4.4814 | ∛90 | Irasional | |
| 91 | 4.4979 | ∛91 | Irasional | |
| 92 | 4.5144 | ∛92 | Irasional | |
| 93 | 4.5307 | ∛93 | Irasional | |
| 94 | 4.5468 | ∛94 | Irasional | |
| 95 | 4.5629 | ∛95 | Irasional | |
| 96 | 4.5789 | 2∛12 | Irasional | |
| 97 | 4.5947 | ∛97 | Irasional | |
| 98 | 4.6104 | ∛98 | Irasional | |
| 99 | 4.6261 | ∛99 | Irasional | |
| 100 | 4.6416 | ∛100 | Irasional |
Want to verify whether any specific integer is an exact cube? Test integers with our instant perfect cube checker →
Penerapan
Penerapan di Dunia Nyata
Akar kubik penting dalam konteks 3 dimensi:
Arsitektur & 3D
Mencari rusuk ruang kubus: ruangan 64 m³ memiliki sisi ∛64 = 4 m.
Logistik & Ekspedisi
Kalkulasi dimensi koli dan berat volumetrik paket.
Fisika & Termodinamika
Jari-jari bola dari volume dan dinamika fluida.
Keuangan & CAGR
Tingkat pertumbuhan tahunan majemuk 3 tahun: r = ∛(Akhir / Awal) - 1.
Keperluan Sehari-hari
Mengetahui panjang rusuk bak penampungan air kubus 27 liter (30 cm).
Under the Hood
How Does This Cube Root Calculator Work?
1
Client-Side High Performance
All calculations execute directly in your browser with zero latency and 100% data privacy.
2
Exact Integer Detection
Instantly checks whether the radicand is a perfect cube and outputs exact integers without rounding drift.
3
Radical Simplification Engine
Performs prime factorization in real time to extract triple factors, rendering exact forms like ∛24 = 2∛3.
4
Full Real Negative Support
Applies the mathematical odd symmetry rule ∛(-x) = -∛x, returning exact real solutions for negative inputs.
5
Arbitrary Precision & Step Workings
Provides clean decimal approximations and comprehensive step-by-step mathematical reasoning.
FAQ
Pertanyaan Umum
What is a cube root?
A cube root of a number is a value that, when multiplied by itself three times, produces the original number. In mathematical notation, the cube root of x is written as ∛x or x^(1/3). For example, the cube root of 27 is 3, because 3 × 3 × 3 = 27.
Can you take the cube root of a negative number?
Yes! Unlike square roots, cube roots of negative numbers are real numbers because multiplying three negative numbers results in a negative product. The rule is ∛(-x) = -∛x. For example, ∛(-8) = -2, because (-2) × (-2) × (-2) = -8.
What is the difference between cubing and taking a cube root?
Cubing and taking the cube root are inverse operations. Cubing a number means raising it to the power of 3 (for example, 4³ = 64). Taking the cube root reverses this process to recover the original base value: ∛64 = 4.
What is a perfect cube?
A perfect cube is an integer that results from multiplying an integer by itself three times. Examples include 1, 8, 27, 64, 125, 216, 343, 512, 729, and 1000. The cube root of a perfect cube is always a whole number.
How do you calculate a cube root without a calculator?
For perfect cubes, use prime factorization: break the number into prime factors, group identical factors into sets of three, and extract one from each group (e.g. 3375 = 3³ × 5³ = 15). For non-perfect cubes, use estimation between the two nearest known perfect cubes.
What is the cube root symbol?
The cube root symbol is ∛ (Unicode character U+221B). It consists of a standard radical sign with a small index 3 in the upper-left notch. In software code it is written cbrt(x), and in LaTeX as \sqrt[3]{x}.
How do you type the cube root symbol?
On Windows, type 221B then press Alt+X in supported apps, or use Character Map. On Mac, press Cmd+Ctrl+Space to open Character Viewer and search 'cube root'. In HTML, use the entity ∛ or copy and paste ∛ directly.
What is ∛0?
The cube root of 0 is exactly 0, because 0 × 0 × 0 = 0.
Is the cube root of 2 rational or irrational?
The cube root of 2 (∛2 ≈ 1.2599) is an irrational number. It cannot be expressed as an exact fraction of two integers, and its decimal expansion continues infinitely without repeating.
What is the cube root of 1?
The real cube root of 1 is 1, since 1 × 1 × 1 = 1. (In complex mathematics, there are also two non-real complex cube roots of unity: e^(2πi/3) and e^(-2πi/3)).
Rangkuman
Kesimpulan Singkat
Inti
Akar pangkat tiga menjawab: bilangan apa yang dikalikan 3 kali menghasilkan nilai ini? Gunakan kalkulator kami untuk hitungan instan.