Square Root (√) & Cube Root (3√) : Example
@@@. Square Root (√) & Cube Root (3√) : Tricks
Q. A solid cuboid has the areas of three adjacent faces as 92 cm², 69 cm², and 75 cm². What is the volume of the cuboid (in cm³) ?
Option : A. 730 B. 843 C. 690 D. 617
Soln
Let the length, breadth, and height of the cuboid be: l, b, h
Given areas of three adjacent faces: lb = 92, bh = 69, hl = 75
To find volume: Volume = lbh
Trick
Multiply all three face areas: (lb)(bh)(hl) = l2b2h2 = (lbh)2
So, Volume2 = 92 × 69 × 75 476100
Now take square root: Volume = 476100 = 690 cm3
Ans: 690 cm3
Q. 3√1860867
Options: 117 127 113 123
Soln: Last digit = 7 → unit digit = 3, Ignore last 3 digits → 1860
Compare cubes: 117³ = 1601613, 123³ = 1860867
Cube root = 123
Ans: 123
Exam Trick
• Last digit → unit digit
• Remaining number → tens digit
• No long calculation needed
Q. 3√0.103823
Options: 0.47 0.46 0.103898 0.47
Soln: Last digit = 7 → unit digit = 3, Ignore last 3 digits → 0.103
Compare cubes of decimals: 0.47³ ≈ 0.103823, Cube root = 0.47
Ans: 0.47
Q. Cube Root of 0.000032768
Options: 0.43 0.032 0.0032 0.00032
Soln: Last digit = 8 → unit digit = 2, Ignore last 3 digits → 0.000032,
Compare cubes of decimals: 0.032³ ≈ 0.000032768, Cube root = 0.032
Ans: 0.032
@@@. Square Root & Cube Root: Tricks
Q. The cube of which number ends in 3 ?
Options: 3 7 9 1
Soln: 7³ = 343 → last digit = 3, Cube root = 7
Ans: 7
Exam Trick
• Last digit → unit digit
• Remaining number → tens digit
• No long calculation needed
@@@. Square Root & Cube Root: Tricks