Viral Maths — Ch08: Cube & Cube Roots

📌 What This Chapter Covers

Book ki seedhi baat: cube of any number ke liye koi trick nahi chahiye — exams mein sirf 1 to 25 tak ke cubes puche jaate hain. Isliye bas yeh 25 values cold yaad karo.
Cube ROOT ke liye ek "Guess Approach" diya gaya hai jo left-part aur units-digit dono ka use karta hai.

⚡ QUICK RECALL

Cube Root Approach directly Ch07 (Square Roots) ke Guess Approach jaisa hai — bas ab teen-teen digits ka group banate hain (kyunki cube hai, square nahi).

🗂️ Chapter Index

Tab	Content
2	Cubes of 1 to 25 — full reference table (memorise, no trick)
3	Cube Root Right Approach — Guess method with units-digit mapping
4	Master Table — everything summarized

🔢 Cubes of Numbers 1 to 25 (Memorise — No Trick Needed)

n	n³	n	n³	n	n³	n	n³	n	n³
1	1	6	216	11	1331	16	4096	21	9261
2	8	7	343	12	1728	17	4913	22	10648
3	27	8	512	13	2197	18	5832	23	12167
4	64	9	729	14	2744	19	6859	24	13824
5	125	10	1000	15	3375	20	8000	25	15625

⚠ EXAM TRAP

Cubes 1–25 ratte maarna hi sabse fast tareeka hai — koi "shortcut" dhundhne ki koshish mat karo, waqt barbaad hoga. Book khud kehti hai: "no trick needed."

Cube Root Right Approach (Guess Method)

Example: ∛12167

Step 1: Break the number leaving 3 digits from the right: 12 | 167 Step 2: Cube of which number is closest to (below) 12? → 2³=8, so tens digit = 2 Step 3: Units digit of 12167 is 7 → which digit's cube ends in 7? → 3³=27, ends in 7 → units digit = 3 Step 4: Combine: 23

⚡ QUICK RECALL — Cube Units-Digit Mapping

Cube ends in: 1 → root ends in 1 Cube ends in: 2 → root ends in 8 Cube ends in: 3 → root ends in 7 Cube ends in: 4 → root ends in 4 Cube ends in: 5 → root ends in 5 Cube ends in: 6 → root ends in 6 Cube ends in: 7 → root ends in 3 Cube ends in: 8 → root ends in 2 Cube ends in: 9 → root ends in 9 Cube ends in: 0 → root ends in 0

⚠ EXAM TRAP

Sirf 2 aur 8, aur 3 aur 7 flip hote hain — baaki digits (1,4,5,6,9,0) apne aap same rehte hain. Yeh cube-root mapping square-root mapping se DIFFERENT hai (square roots mein 1↔9 aur 4↔8 tha) — dono ko mix mat karo.

📋 Master Table — Chapter 8 Summary

Topic	Approach
Cube of a number	No trick — memorise cubes 1–25 directly
Cube root	Split leaving 3 digits from right → left part gives tens digit (nearest cube below) → units digit uses the cube-ending map

🔑 Cube Units-Digit Quick Reference

Cube ends in	0	1	2	3	4	5	6	7	8	9
Root ends in	0	1	8	7	4	5	6	3	2	9