Calculate it without your pen or calculator

So far, we have learnt the trick of squaring two-digit numbers that end in 5.  Today we are going to learn how to square a two-digit number that ends in 1.

The answer is written from ‘right to left’ in three steps :

Step 1 : The answer ends in 1.

Step 2 : Double the first digit and put to the left of the above 1.

Step 3 : Square the first digit and put to the left of all the above.

Example 1 : Find the square of 31.

3 × 2 = 6   (Step 2)

3² =9   (Step 3)

Therefore, 31² = 961

Example 2 : Find the square of 41.

4 × 2 = 8   (Step 2)

4² = 16   (Step 3)

Therefore, 41² = 1681

If you get more than one digit in steps  2 and 3, just put down the right-side digit and carry the rest.

Example 3 : Find the square of 51.

5 × 2 = 10 .   So,  just put down 0 and carry 1 to the next step.

5² = 25

25 + 1 = 26

Therefore, 51² = 2601 

Ok, verify the following :

61² = 3721     ( 36 ¦ 12 ¦ 1 )

71² = 5041    ( 49 ¦ 14 ¦ 1 )

Actually, this method can be applied to more than two-digit number, as long as it ends in 1.

Example 4 :      121² = 14641     ( 144 ¦ 24 ¦ 1 ) 

Master the two-digit numbers first before you practise the more challenging one.  Good luck🙂

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Posted on March 18, 2009, in Info Matematik. Bookmark the permalink. 3 Comments.

  1. teacher,how if the number is with decimal number but also end with 1 also?

    • We still can use the same method, Chu Ting. Just move the decimal point accordingly.

      For example,
      the answer for 3.1 X 3.1 (which is 3.1 square)should be in two decimal places.

      Since 31 X 31 = 961
      Therefore 3.1 X 3.1 = 9.61,
      and 0.31 X 0.31 = 0.0961

  2. o..ok..i get it now..haha..thanks so much..teacher..

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