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) = l2b2h = (lbh)2


So, Volume2 = 92 × 69 × 75 476100


Now take square root: Volume = 476100 = 690 cm3


Ans: 690 cm3


Q. 31860867 


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. 30.103823 


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