# 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 = 26**0**1

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 🙂

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

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

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