Sublime Maths Worksheets

Finding the square of a number

Finding the square of a number

Introduction

This mathematics trick helps you calculate the squares of the numbers in your mind. Once it is learnt, you can easily write down the squares of the numbers up to 300.

What you need to know before you start...

You need to master Multiplication Tables (1 to 20) and Squares (1 to 30). Memorizing these essential concepts is crucial for any mathematics student. Our specially crafted worksheets on Multiplication and Squares will help you solidify this knowledge. Not only will it benefit this blog post, but it will also prove invaluable for numerous other topics covered on our blog.
Use the Times Tables Reference to learn and memorize.

The steps are...

Choose a number as an example to understand the steps:
Finding the value of 642...
Step 1:

Imagine the given number is composed of two parts.

Let all the digits except the unit digit be the 1st part A.

Let the unit digit be the 2nd part B.

Let AB = 64 be the given number where:

A = 6

B = 4

Take the unit digit B and square it.Here B = 4
B2 = C1O142 = 16

Where C1 is the carry over and O1 is the output from this step.

Where C1 = 1 and O1 = 6

642 is ???6
Step 2:
Multiply the number 2, the 1st part A and the 2nd part B together. To this product, add the carry over C1 from Step 1.Here A = 6, B = 4 and C1 = 1

(2 ✕ A ✕ B) + C1 = C2O2

(2 ✕ 6 ✕ 4) + 1 = 49

Where C2 is the carry over and O2 is the output from this step.

Where C2 = 4 and O2 = 9

642 is ??96
Step 3:
Take the 1st part A, square it and add C2 from Step 2 to it.Here A = 6 and C2 = 4

A2 + C2 = O3

62 + 4 = 40

Where O3 is the output from this step.Where O3 = 40
642 is 4096

Quick application of the steps on all the given numbers

StepFinding 282Carry OverAnswer
182 = 646??4
2(2 ✕ 2 ✕ 8) + 6 = 383?84
322 + 3 = 7 784
StepFinding 392Carry OverAnswer
192 = 818???1
2(2 ✕ 3 ✕ 9) + 8 = 626??21
332 + 6 = 15 1521
StepFinding 472Carry OverAnswer
172 = 494???9
2(2 ✕ 4 ✕ 7) + 4 = 606??09
342 + 6 = 22 2209
StepFinding 552Carry OverAnswer
152 = 252???5
2(2 ✕ 5 ✕ 5) + 2 = 525??25
352 + 5 = 30 3025
StepFinding 642Carry OverAnswer
142 = 161???6
2(2 ✕ 6 ✕ 4) + 1 = 494??96
362 + 4 = 40 4096
StepFinding 712Carry OverAnswer
112 = 10???1
2(2 ✕ 7 ✕ 1) + 0 = 141??41
372 + 1 = 50 5041
StepFinding 832Carry OverAnswer
132 = 90???9
2(2 ✕ 8 ✕ 3) + 0 = 484??89
382 + 4 = 68 6889
StepFinding 922Carry OverAnswer
122 = 40???4
2(2 ✕ 9 ✕ 2) + 0 = 363??64
392 + 3 = 84 8464
StepFinding 1082Carry OverAnswer
182 = 646????4
2(2 ✕ 10 ✕ 8) + 6 = 16616???64
3102 + 16 = 116 11664
StepFinding 1122Carry OverAnswer
122 = 40????4
2(2 ✕ 11 ✕ 2) + 0 = 444???44
3112 + 4 = 125 12544
StepFinding 1362Carry OverAnswer
162 = 363????6
2(2 ✕ 13 ✕ 6) + 3 = 15915???96
3132 + 15 = 184 18496
StepFinding 1482Carry OverAnswer
182 = 646????4
2(2 ✕ 14 ✕ 8) + 6 = 23023???04
3142 + 23 = 219 21904
StepFinding 1522Carry OverAnswer
122 = 40????4
2(2 ✕ 15 ✕ 2) + 0 = 606???04
3152 + 6 = 231 23104
StepFinding 1632Carry OverAnswer
132 = 90????9
2(2 ✕ 16 ✕ 3) + 0 = 969???69
3162 + 9 = 265 26569
StepFinding 1752Carry OverAnswer
152 = 252????5
2(2 ✕ 17 ✕ 5) + 2 = 17217???25
3172 + 17 = 306 30625
StepFinding 2242Carry OverAnswer
142 = 161????6
2(2 ✕ 22 ✕ 4) + 1 = 17717???76
3222 + 17 = 501 50176
StepFinding 2582Carry OverAnswer
182 = 646????4
2(2 ✕ 25 ✕ 8) + 6 = 40640???64
3252 + 40 = 665 66564

The trick behind this trick

This trick is nothing but the application of the classic algebraic identity

(a + b)2 = a2 + 2ab + b2

Our worksheets

Once you've learnt this trick, please do visit Practice drill on squares worksheet page and put your learnings into practice.