by When we write x*x*x, it simply means we are multiplying the number x by itself three times. In mathematical notation, this is written as x³ (x cubed). So the equation:
x * x * x = 2 → x³ = 2
This is a cubic equation — one of the most fundamental types in algebra. The question is: what number, when multiplied by itself three times, gives exactly 2?
Quick Concept: Just like x² = 4 means x = √4 = 2, similarly x³ = 2 means x = ∛2 (the cube root of 2).
This type of problem appears in CBSE Class 8, 9, and 10 Mathematics, in competitive exams like JEE Mains, and even in daily life situations involving volume and scaling. Understanding it deeply will help you solve entire families of equations.
KEY POINTS
How to Solve x*x*x = 2 (Step-by-Step)
Solving x³ = 2 requires finding the cube root of 2. Let’s walk through it clearly:
Method 1 — Using Cube Root
Step 1Write the equation: x³ = 2
Step 2Take cube root on both sides: ∛(x³) = ∛2
Step 3Left side simplifies: x = ∛2
Resultx = ∛2 = 2^(1/3) ≈ 1.2599
Method 2 — Using Exponent Rules
Step 1x³ = 2
Step 2Raise both sides to power (1/3): (x³)^(1/3) = 2^(1/3)
Step 3x^(3×1/3) = 2^(1/3)
Step 4x^1 = 2^(1/3)
Resultx = 2^(1/3) ≈ 1.25992105…
Method 3 — Trial & Estimation (For Mental Math)
We know:
- 1³ = 1 (too small)
- 1.2³ = 1.728 (getting close)
- 1.26³ = 2.000376 (very close!)
- 1.2599³ ≈ 2.000 ✅
So by estimation, x lies between 1.2 and 1.3, and more precisely x ≈ 1.2599.
The Exact & Approximate Answer
Exact Answer
x = ∛2 = 2^(1/3)
Decimal Approximation: x ≈ 1.25992105…
The value ∛2 is an irrational number — like π or √2, it cannot be expressed as a simple fraction. Its decimal expansion is infinite and non-repeating. For most exam purposes (CBSE, JEE), we use:
x ≈ 1.2599 (correct to 4 decimal places)
The number also has two complex (imaginary) roots, but for school-level mathematics in India, we only consider the real root x = ∛2.“`
Cube Root Value Table
To understand where x³ = 2 fits, here is a complete cube root reference table:
| Number (n) | n³ = ? | ∛n = ? | Type |
|---|---|---|---|
| 1 | 1 | 1.000 | Perfect Cube ✅ |
| 2 | 8 | 1.2599 | Irrational 🔥 |
| 3 | 27 | 1.4422 | Irrational |
| 4 | 64 | 1.5874 | Irrational |
| 5 | 125 | 1.7100 | Irrational |
| 8 | 512 | 2.000 | Perfect Cube ✅ |
| 27 | 19683 | 3.000 | Perfect Cube ✅ |
Note for CBSE students: Perfect cubes (1, 8, 27, 64, 125…) have whole number cube roots. The number 2 is NOT a perfect cube, so ∛2 is irrational.
Real-World Examples of x³ = 2
Example 1 — Box Volume
Suppose you have a cubic box whose volume is 2 cubic metres. What is the length of one side? Since Volume = side³, we solve side³ = 2, giving side = ∛2 ≈ 1.26 metres.
Example 2 — Computer Science (Scaling)
In algorithm analysis, if an operation scales as O(n³) and you want it to process exactly twice the data (factor of 2), you scale n by ∛2 ≈ 1.26 — meaning you need 26% more input size.
Example 3 — Chemistry (Crystal Lattice)
In crystallography, unit cells are cubic. If a cell has volume 2 ų, the edge length is ∛2 ≈ 1.26 Å. This appears in solid-state chemistry problems in Class 12 and JEE Advanced.
Example 4 — Economics (Growth Rate)
If an investment triples its cubed value in 3 years and you want the year 1 factor, you solve x³ = 2 — giving a per-year growth factor of approximately 1.26×.
Also Read: Exploring the Tech Innovations Powering Non-Invasive Treatments
हिंदी में समझाया — x*x*x = 2
🇮🇳हिंदी | Hindi
जब हम लिखते हैं x*x*x = 2, तो इसका मतलब है कि किसी संख्या x को तीन बार खुद से गुणा करने पर 2 आता है। गणित में इसे x³ = 2 लिखते हैं।
इसे हल करने के लिए हम दोनों तरफ का घनमूल (cube root) लेते हैं:
x = ∛2 = 2^(1/3) ≈ 1.2599
यह संख्या एक अपरिमेय संख्या (irrational number) है, जैसे √2 या π। इसे किसी साधारण भिन्न (fraction) में नहीं लिखा जा सकता।
CBSE कक्षा 8–10 के छात्रों के लिए: घनमूल की परिभाषा याद रखें — वह संख्या जिसे तीन बार गुणा करने पर दी गई संख्या मिले। जैसे ∛8 = 2 क्योंकि 2×2×2 = 8। इसी प्रकार, ∛2 ≈ 1.2599 क्योंकि 1.2599 × 1.2599 × 1.2599 ≈ 2 होता है।
தமிழில் விளக்கம் — x*x*x = 2
🇮🇳தமிழ் | Tamil
x*x*x = 2 என்பதன் பொருள்: x என்ற எண்ணை மூன்று முறை பெருக்கும்போது 2 கிடைக்கிறது என்பதாகும். கணிதத்தில் இதை x³ = 2 என எழுதுவோம்.
தீர்வு காண: இரு பக்கங்களிலும் கன மூலம் (cube root) எடுக்கவும்:
x = ∛2 ≈ 1.2599
இந்த எண் ஒரு அகன்ற எண் (irrational number) — அதாவது இதை எளிய பின்னமாக (fraction) எழுத இயலாது.
CBSE மாணவர்களுக்கு: ∛8 = 2 ஏனெனில் 2×2×2 = 8. அதுபோல், ∛2 ≈ 1.2599 ஏனெனில் 1.2599³ ≈ 2.
తెలుగులో వివరణ — x *x*x = 2
🇮🇳తెలుగు | Telugu
x*x*x = 2 అంటే: x అనే సంఖ్యను మూడుసార్లు గుణించినప్పుడు 2 వస్తుంది అని అర్థం. గణితంలో దీన్ని x³ = 2 అని రాస్తాం.
సాధించడానికి: రెండు వైపులా ఘనమూలం (cube root) తీసుకోండి:
x = ∛2 ≈ 1.2599
ఈ విలువ ఒక అకరణ సంఖ్య (irrational number) — దీన్ని సాధారణ భిన్నంగా వ్యక్తపరచలేం.
CBSE విద్యార్థులకు: ∛8 = 2 ఎందుకంటే 2×2×2 = 8. అదే విధంగా, ∛2 ≈ 1.2599 ఎందుకంటే 1.2599³ ≈ 2.
বাংলায় ব্যাখ্যা — x*x*x = 2
🇮🇳বাংলা | Bengali
x*x*x = 2 মানে হলো: x সংখ্যাটিকে তিনবার গুণ করলে 2 পাওয়া যায়। গণিতে এটিকে x³ = 2 লেখা হয়।
সমাধান করতে: উভয় পক্ষের ঘনমূল (cube root) নিন:
x = ∛2 ≈ 1.2599
এই মানটি একটি অমূলদ সংখ্যা (irrational number) — অর্থাৎ এটিকে সাধারণ ভগ্নাংশে প্রকাশ করা সম্ভব নয়।
CBSE শিক্ষার্থীদের জন্য: ∛8 = 2 কারণ 2×2×2 = 8। ঠিক তেমনি, ∛2 ≈ 1.2599 কারণ 1.2599³ ≈ 2।
Frequently Asked Questions
x = ∛2 = 2^(1/3) ≈ 1.25992105. This is the real cube root of 2 and it is an irrational number.
Yes, exactly. x*x*x means x multiplied by itself 3 times, which is the definition of x³ (x cubed).
∛2 is irrational. It cannot be expressed as p/q where p and q are integers. Its decimal form (1.25992105…) is infinite and non-repeating.
Use the ∛ button, or enter: 2 ^ (1÷3). On a scientific calculator, press 2, then shift/2nd, then x³. On Google, search “cube root of 2”.
हाँ! x = ∛2 ≈ 1.2599. यह एक वास्तविक और अपरिमेय संख्या है। इसे कैलकुलेटर पर 2^(1/3) से निकाल सकते हैं।
In real numbers, there is only one real solution: x = ∛2 ≈ 1.2599. However, in complex numbers (higher mathematics), there are two additional complex roots. For CBSE and school-level maths, only the real root matters.
x² = 2 gives x = ±√2 ≈ ±1.4142 (two real solutions). x³ = 2 gives x = ∛2 ≈ 1.2599 (one real solution). The cube root is smaller than the square root in this case because cubing grows faster than squaring.
Cube and cube roots are covered in CBSE Class 8 Mathematics, Chapter 7 (Cube and Cube Roots). Solving cubic equations appears in Class 9 and 10 Algebra chapters as well.
Conclusion
The equation x*x*x = 2 (i.e., x³ = 2) is a beautiful and fundamental problem in mathematics. Its solution — x = ∛2 ≈ 1.2599 — is an irrational number that appears across algebra, geometry, physics, chemistry, and even computer science.
For Indian students preparing for CBSE, JEE, or NEET, mastering cube roots and cubic equations is essential. Whether you’re in Class 8 learning cube roots for the first time, or a JEE aspirant dealing with polynomial equations — the concept of x³ = 2 is a stepping stone to deeper mathematical understanding.
📌 Remember: x*x*x = x³ | x³ = 2 means x = ∛2 | ∛2 ≈ 1.2599 | It is an irrational number.
