Viral Maths — Ch08: Cube & Cube Roots

📌 What This Chapter Covers

The book states plainly that no trick is needed to find cubes. Exams ask only the cubes from 1 to 25, so memorize these 25 values perfectly.
For cube roots, a Guess Approach is provided that uses both the left part and the units digit.

⚡ QUICK RECALL

The Cube Root Approach resembles the Guess Approach in Chapter 7. Here, however, digits are grouped in sets of three because the operation concerns cubes rather than squares.

🗂️ 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

Memorizing the cubes from 1 to 25 is the fastest method. Do not waste time searching for a shortcut; the book itself says that no trick is 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

Only 2 and 8, and 3 and 7, are reversed; the remaining digits (1, 4, 5, 6, 9 and 0) remain unchanged. This cube-root mapping is DIFFERENT from the square-root mapping, where 1↔9 and 4↔8. Do not mix them.

📋 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