What is the short trick to solve cube root and to do cubes of number and squares of number
1. Cube Root Trick (For Perfect Cubes)
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Memorize the cubes of numbers from 1 to 10.
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Example: 1 = 1, 2 = 8, 3 = 27, …, 10 = 1000
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Break the number into the last digit and the remaining part.
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Example: Find the cube root of 59319
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Last digit is 9 → Cube of 9 is 729, so unit place = 9
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Remaining number 59 → Lies between 3 × 3 × 3 = 27 and 4 × 4 × 4 = 64, so tens digit = 3
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Answer: 39
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2. Shortcut to Find Cubes
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Use (a + b) × (a + b) × (a + b) = a × a × a + 3 × a × a × b + 3 × a × b × b + b × b × b
Example: 13 × 13 × 13
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Split as (10 + 3) × (10 + 3) × (10 + 3)
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= 10 × 10 × 10 + 3 × 100 × 3 + 3 × 10 × 9 + 3 × 3 × 3
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= 1000 + 900 + 270 + 27 = 2197
3. Shortcut for Squares of Numbers
A) For numbers ending in 5
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(N5) × (N5) = N × (N + 1) followed by 25
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Example: 35 × 35 → 3 × 4 followed by 25 = 1225
B) For any number (Close to a base)
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(N + x) × (N + x) = N × N + 2 × N × x + x × x
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Example: 41 × 41
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40 × 40 = 1600
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2 × 40 × 1 = 80 , and 1 × 1 = 1
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1600 + 80 + 1 = 1681
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