16. Squaring Decimal Numbers : Ex: (1.2)² Ex: (2.35)² Ex 3: (0.07)²


Shortcut for Squaring Decimal Numbers (āĻĻāĻļāĻŽāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻžā§° āĻŦā§°ā§āĻ— āϕ⧰āĻžā§° āϏāĻšāϜ āĻ•ā§ŒāĻļāϞ)


Rule (āύāĻŋāϝāĻŧāĻŽ)



  1. Ignore the decimal point and square the number as an integer. (āĻĻāĻļāĻŽāĻŋāĻ• āĻŦāĻŋāĻ¨ā§āĻĻ⧁āĻŸā§‹ āϏāĻžāĻŽāϝāĻŧāĻŋāĻ•āĻ­āĻžā§ąā§‡ āφāρāϤ⧰āĻžāχ āϏāĻ‚āĻ–ā§āϝāĻžāĻŸā§‹āĻ• āĻĒā§‚ā§°ā§āĻŖāϏāĻ‚āĻ–ā§āϝāĻž āĻšāĻŋāϚāĻžāĻĒ⧇ āĻŦā§°ā§āĻ— āϕ⧰āĻ•āĨ¤)

  2. Count the decimal places in the original number. (āĻŽā§‚āϞ āϏāĻ‚āĻ–ā§āϝāĻžāϤ āĻĨāĻ•āĻž āĻĻāĻļāĻŽāĻŋāĻ• āϘ⧰⧰ āϏāĻ‚āĻ–ā§āϝāĻž āĻ—āĻŖāύāĻž āϕ⧰āĻ•āĨ¤)

  3. Put double the decimal places in the final answer. (āωāĻ¤ā§āϤ⧰āϤ āϤāĻžā§° āĻĻ⧁āϗ⧁āĻŖ āĻĻāĻļāĻŽāĻŋāĻ• āϘ⧰ ā§°āĻžāĻ–āĻ•āĨ¤)


Ex: (1.2)²



  • Ignore decimal: 122=144

  • 1 decimal place → Answer must have 2 decimal places

  • Ans: 1.44


Ex: (2.35)²



  • Ignore decimal: 2352=55225

  • 2 decimal places → Answer must have 4 decimal places

  • Ans: 5.5225


Ex 3: (0.07)²



  • Ignore decimal: 72=49

  • 2 decimal places → Answer must have 4 decimal places

  • Ans: 0.0049


This method works for all decimal numbers.


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MCQs


1. What is 0.4² ? (0.4² āĻ•āĻŋāĻŽāĻžāύ ?)


A) 0.16 B) 0.04 C) 1.6 D) 0.0016


Ans/āωāĻ¤ā§āϤ⧰: A) 0.16


Explanation: 4² = 16, original decimal place = 1, so answer has 2 decimal places → 0.16. āĻŦā§āϝāĻžāĻ–ā§āϝāĻž: 4² = 16, āĻŽā§‚āϞ āϏāĻ‚āĻ–ā§āϝāĻžāϤ ā§§āϟāĻž āĻĻāĻļāĻŽāĻŋāĻ• āϘ⧰ āφāϛ⧇, āϏ⧇āϝāĻŧ⧇āĻšā§‡ āωāĻ¤ā§āϤ⧰āϤ ⧍āϟāĻž āĻĻāĻļāĻŽāĻŋāĻ• āϘ⧰ āĻĨāĻžāĻ•āĻŋāĻŦ → 0.16āĨ¤


2. What is 1.5² ? 1.5² āĻ•āĻŋāĻŽāĻžāύ ?

A) 2.15 B) 2.25 C) 1.25 D) 3.25


Ans/āωāĻ¤ā§āϤ⧰: B) 2.25


Explanation: 15² = 225, original decimal place = 1, so answer has 2 decimal places → 2.25. āĻŦā§āϝāĻžāĻ–ā§āϝāĻž: 15² = 225, āĻŽā§‚āϞ āϏāĻ‚āĻ–ā§āϝāĻžāϤ ā§§āϟāĻž āĻĻāĻļāĻŽāĻŋāĻ• āϘ⧰ āφāϛ⧇, āϏ⧇āϝāĻŧ⧇āĻšā§‡ āωāĻ¤ā§āϤ⧰āϤ ⧍āϟāĻž āĻĻāĻļāĻŽāĻŋāĻ• āϘ⧰ āĻĨāĻžāĻ•āĻŋāĻŦ → 2.25āĨ¤


Remember (āĻŽāύāϤ ā§°āĻžāĻ–āĻŋāĻŦāĻž)

Ignore Decimal → Square the Number → Double the Decimal Places (āĻĻāĻļāĻŽāĻŋāĻ• āφāρāϤ⧰āĻžāĻ“ → āϏāĻ‚āĻ–ā§āϝāĻžāĻŸā§‹ āĻŦā§°ā§āĻ— āϕ⧰āĻž → āĻĻāĻļāĻŽāĻŋāĻ• āϘ⧰ āĻĻ⧁āϗ⧁āĻŖ āϕ⧰āĻž)


Magic Formula: Decimal places in answer = 2 × Decimal places in original number


This works for all decimal squares. (āĻāχ āύāĻŋāϝāĻŧāĻŽ āϏāĻ•āϞ⧋ āĻĻāĻļāĻŽāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻžā§° āĻŦā§°ā§āĻ—ā§° āĻŦāĻžāĻŦ⧇ āĻĒā§ā§°āϝ⧋āĻœā§āϝāĨ¤)