# Square and Square Root of three digit get using formula 1

Shortcut Tricks are very important things in competitive exam. Time takes a huge part in competitive exams. If you know time management then everything will be easier for you. Most of us miss that part. Here in this page we give few examples on Square and Square Root of three digit shortcut tricks. These shortcut tricks cover all sorts of tricks on Square and Square Root of three digit. Visitors please read carefully all shortcut examples. These examples here will help you to better understand shortcut tricks on square and square root of three digit.

Before starting anything just do a math practice set. Write down twenty math problems related to this topic on a page. Do first ten maths using basic formula of this math topic. You also need to keep track of the time. After finish write down total time taken by you to solve those ten maths. Now go through our page for square and square root of three digit shortcut trick. After doing this go back to the remaining ten questions and solve those using shortcut methods. Again keep track of the time. You will surely see the improvement in your timing this time. But this is not all you want. If you need to improve your timing more then you need to practice more.

### Few important things about Three digit Square Root

Math section in a competitive exam is the most important part of the exam. That doesn’t mean that other sections are not so important. But if you need a good score in exam then you have to score good in maths. You can get good score only by practicing more and more. You should do your math problems within time with correctness, and only shortcut tricks can give you that success. Again it does not mean that you can’t do maths without using shortcut tricks. You may do math problems within time without using any shortcut tricks. You may have that potential.

But, so many other people may not do the same. For those we prepared this square and square root of three digit shortcut tricks. We always try to put all shortcut methods of the given topic. But if you see any tricks are missing from the list then please inform us. Your little help will help others.

Square and Square Root both are very important in any competitive exams. Square and Square Root Shortcut Tricks Without remembering this you can’t survive in exam hall. As all competitive exams are very tightly bound with time,we discuss the using formula and how we get the result of square and square root of three digit using formula 1, lets how the formula that can easily obtain the answer of Square and Square Root of three digit.

### Square and Square Root using formula

**Formula:** (a + b)^{2} = a^{2} + 2ab + b^{2}

i.e, (a / b)^{2} = a^{2} / 2ab / b^{2} *[We replace ‘+’ sign with ‘/’]*

We will apply this formula to obtain the square of a Three digit number.

### Example #1 – Square and Square Root of Three digit number

(122)^{2} = ?

- 14884
- 15782
- 16339
- 17344

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (A)

**How to Solve**

- Firstly break the number into two parts and Consider a = 12 and b = 2.
- Applying formula,

a^{2}+ 2ab + b^{2}

OR

a^{2}/ 2ab / b^{2}

= 12^{2}/ 2 x 12 x 2 / 2^{2}

= 144 / 48 / 4 - Go from Right to Left

Note down 4 and Carry 0. - Add carry 0 with 48,

i.e, (0 + 48) = 48, Note down 8 at the left of 4 and Carry 4. - Add carry 4 with 144,

i.e, (4 + 144) = 148, Note down 148 at the left of 8.

So, We get our answer (122)^{2}= 14884.

**Rough Workspace**

### Example #2 – Square and Square Root of Three digit number

(114)^{2} = ?

- 10447
- 11558
- 12996
- 13684

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (C)

**How to Solve**

- Firstly break the number into two parts and Consider a = 11 and b = 4.
- Applying formula,

a^{2}+ 2ab + b^{2}

OR

a^{2}/ 2ab / b^{2}

= 11^{2}/ 2 x 11 x 4 / 4^{2}

= 121 / 88 / 16 - Go from Right to Left

Note down 6 and Carry 1. - Add carry 1 with 88,

i.e, (1 + 88) = 89, Note down 9 at the left of 6 and Carry 8. - Add carry 8 with 121,

i.e, (8 + 121) = 129, Note down 129 at the left of 9.

So, We get our answer (114)^{2}= 12996.

**Rough Workspace**

### Example #3

(223)^{2} = ?

- 47332
- 49729
- 51743
- 53982

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (B)

**How to Solve**

- Firstly break the number into two parts and Consider a = 22 and b = 3.
- Applying formula,

a^{2}+ 2ab + b^{2}

OR

a^{2}/ 2ab / b^{2}

= 22^{2}/ 2 x 22 x 3 / 3^{2}

= 484 / 132 / 9 - Go from Right to Left

Note down 9 and Carry 0. - Add carry 0 with 132,

i.e, (0 + 132) = 132, Note down 2 at the left of 9 and Carry 13. - Add carry 13 with 484,

i.e, (13 + 484) = 497, Note down 497 at the left of 2.

So, We get our answer (223)^{2}= 49729.

**Rough Workspace**

### Example #4

(125)^{2} = ?

- 11268
- 13734
- 15625
- 18932

Show Answer Show How to Solve Open Rough Workspace

**Answer:**Option (C)

**How to Solve**

- Firstly break the number into two parts and Consider a = 12 and b = 5.
- Applying formula,

a^{2}+ 2ab + b^{2}

OR

a^{2}/ 2ab / b^{2}

= 12^{2}/ 2 x 12 x 5 / 5^{2}

= 144 / 120 / 25 - Go from Right to Left

Note down 5 and Carry 2. - Add carry 2 with 120,

i.e, (2 + 120) = 122, Note down 2 at the left of 5 and Carry 12. - Add carry 12 with 144,

i.e, (12 + 144) = 156, Note down 156 at the left of 2.

So, We get our answer (125)^{2}= 15625.

**Rough Workspace**

### You may also like to know:

- Square and Square Root of two digit get using formula 1
- 100 base method Square and Square Root
- Square and Square root a number ending with 6
- << Go back to Square and Square Root main page

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If You Have any question regarding this topic then please do comment on below section. You can also send us message on facebook.

Sir ur tricks are really very helpful….

But in (998)2 i.e 998×998 the trick suggested by u is failed. Plz help…

You can do this way

998 x 998

998 x 9 = 8982 add two zero

998 x 9 = 8982 add one zero

998 x 8 = 7984

Add all three together

898200 + 89820 + 7984 = 996004

Short Process

998 * 998 = 99604

1000-998=2

2 x 2 = 4

998-2=996

99604 answer

Wao u r grt can u send some tips else.

answer should be 996004

wrong answer

if its 100 then prefix one zero to 4, since its 1000, prefix 2 zeros to 4 to make it a three digit number. then subtract 2 from 998,which is 996, so 996004

I know this is a abacus trick😃

Well done

Hi Priya,l The trick is working on 998 also. Plz check

for the numbers around 1000 we should add three digits in the last

for eg

1.998 (1000-2)

2*2=4 so 004 and 998-2=996

so answer is 996004

2.992 (1000-8)

8*8=064 and 992-8=984

answer is 984064

99*99/2*99*8/8*8

9801/1584/64

9960 0 4 this trick. never fails

but for this we should first calculate 99 square

use base 1000 method

998 -002

998 -002

____________________

(998-02)/(-002*-002)

996/004 is the answer

u solved it wrong

the trick works accurately till 999 correct yourself

114^2= base 100..,,114 is moew than 100 by 14.

step1: add 14 to 114….114+14=128

step 2: square of 14.,..,196..now put it in last…and carry 1…

final result is 12996.

same with numbers which are less than 100.

98^2= 100-98=2

now 98-2=”96″

2^2=”4″

put is at last..answer is 9604…remember to put a zero before 4… 🙂 😉 🙂

you can also do like this;

(998)2=(1000-2)2 i.e. (a-b)2

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

=(1000)2 – 2(1000×2) + (2)2

=1000000 – 4000 + 4

=996004

Helpfull

√11256 plz tell how to solve.this is not perfect square

No its not a perfect square

very helpful..thanks..

for squre

for Example: squre of 30

Ans: 30 x 30=900

E.g. 33

Ans: 33 x 33= 1089

My shortcut:

(999)2 = (1000)2 – 1000 – 999

(998)2 = (1000)2 -1000 – 999 – 999 – 998

or

(998)2 = (999)2 – 999 – 998

Likewise

(1001)2 = (1000)2 + 1000 + 1001

(1002)2 = (1001)2 + 1001 + 1000

To know (84)2,

We know (85)2 = 7225 (hope you know this)

(84)2 = 7225 – 85 – 84 = 8056.

(31)2 = (30)2 + 30 + 31

To find square root, there is an easy method available.

Hi can u pls give a trick to solve square of 579 ?

plz 122 square give with solution .

122 square = (12)square + 2 x 12 x 2 + (2)square

= 144 + 48 + 4 = 14884

follow the given steps you can get the ans.

awesome trick sir mindblowing

it is v useful.thank you.also want some tricks for squre roots.its too hrd

pls give me square root of 1225. also give me the short trick for find square root of 5,6,7 digit

i want too

Plz give me square root of 326. Ur trick is not working

it’s a very helpful trick sir…thank u so much….

well its good. but i would like to share more about this…like if we want to find the value of sqare root. like 15625 = (?)^2.

so we simply take last digit which is “5”.

so now we got one value whose square having 5 in last,

and that is “5”.

put that 5 in last,

Now

take first 3 digits from 15625, which is 156

and the near by square value is 12^2=144

so the ans will be 125.

Hey Guys!!

Hope you are doing Great!!

I have 3 digit no. 513, Please let me know square of this in shortcut keys.

Thanks in advance.

Deepak

Thank you sir

. Its very helpful