Square And Square Root Shortcut Tricks

Square And Square Root Shortcut Tricks

Square and Square Root of two digit get using formula1

Square and Square Root get using formula

Formula: (a+b)2 = a2+2ab+b2 i.e, (a / b)2= a2 / 2ab / b2
we applied this formula to obtain the square of a number

Example 1:
( 57 )2

= ( 5 / 7 )2
Answer :
Apply formula of a2+2ab+b2
Consider,
572 = ?
A as 5
B as 7 (we break the number in two parts i.e, A as 5 and B as 7 and applied formula )
= 52 / 2 x 5 x 7 / 72
= 25 / 2 x 5 x 7 / 49
a2= 25
b2= 49
2ab = 2 x 5 x 7 = 70
= 25 / 70 / 49
 

Step 1: Put down 9 carry 4
 

Step 2: add carry 4 to 70 = 74 put down 4 carry 7
 

Step 3: add carry 7 to 25 = 32 put down 32
and answer is 3249,
= 3249

All this do on your mind which will help in fast calculation to obtain the answer of Square and Square Root of a number.
we applied this formula to obtain the square of a number

 

This is similar to the above Example.

 

Example 2:
(69)2
= (6/9)2
Answer :
Consider A as 6, and B as 9.
= 62 / 2 x 6 x 9 / 92
= 36 / 2 x 6 x 9 / 81 (we break the number in two parts i.e, A as 6 and B as 9 and applied formula )
a2 = 36
b2= 81
2ab = 2 x 6 x 9 = 108
=36 / 108 / 81

Step1: put down 1 carry 8
 

Step2 : add 8 to 108 =116 then put down 6 carry 11

Step3 : and add 11 to 36 = 47 and put down 47
= so answer is 4761,
= 4761

Note: All this do on your mind which will help in fast calculation to obtain the answer of Square and Square Root of a number.

 

Square and Square Root of three digit get using formula1

we applied this formula to obtain the square of three digit number
 

Example 1:
 

Square and Square Root of 1142

Answer :
Firstly we separate the 114 like this (11/4)2
then applied previous formula on it

=112 / 2x11x4 / 42
=112 / 2x11x4 / 16
=121 / 88 / 16
=12996
we apply the formula a2 + 2.a.b + b2
 

Step 1: note down 6 carry 1
 

Step 2: add carry 1 to 88 =  89, note down 9 carry 8.
 

Step 3: add carry 8 to 121 and note down 129
= 12996

Note: we can also separate 114 to find square like (1/14)2

 

Example 2:
 

Square and Square Root of 2232

Answer :
Firstly we separate the 223 like this(22/3)2

then applied previous formula on it
we apply the formula a2 + 2.a.b + b2
= 222 + 2 x 22 x 3 + 32
=484 / 132 / 9
= 49729

Step 1: note down 9
 

Step 2:note down 2 carry 13.
 

Step 3:add carry 13 to 4 = 17, note down 7
 

Step 4: add carry 1to 48 = 49 put down

= 49729

 

Note: All this do on your mind which will help in fast calculation to obtain the answer of Square and Square Root of a number.

 

Square and Square Root of 100 base method

Example 1: 982= ?
Answer :
 

Step 1: First we know that 982 is double of 98 that is = 98 x 98 = ?,
At first we count the number of less from 100. that is the above 98 is 2 less from 100.
 

Step2: Now we are going to multiply 2 x 2 = 4 and note down this 4 ( that are come from both less 98 x 98 from 100).
 

Step 2: put one Zero left from 4 and now subtract the less number is 2 from 98 that is = 96and the answer is 9604.

 

Example 2 : 962 = ?
Answer :
 

Step 1: First we know that 962 is double of 96 that is = 96 x 96 = ?,
At first we count the number of less from 100. that is the above 96 is 4 less from 100.
 

Step 2: Now we are going to multiply 4 x 4= 16 and note down this 16 ( that are come from both less 96 x 96 from 100).
 

Step 3: now subtract the less number is 4 from 96 that is = 92 and put down it
that is 9261

and the answer is 9216.

 

Square and Square root a number ending in 6

 

Example 1:
762
 

Step 1:put down 6
 

Step 2:Multiply 2 with (7 + 1) = 16 and add 16 +1 = 17.put down 7 and carry 1 .
 

Step 3:Multiply 7 with (7 + 1) = 56 + carry 1 = 57 put down 57
Answer is 5776

 

Example 2:
962
 

Step 1:put down 6
 

Step 2:Multiply 2 with (9 + 1) = 20 and add 20 + 1 = 21.put down 1 and carry 2 .
 

Step 3:Multiply 9 with (9 + 1) = 90 + carry 2 = 92 put down 92
Answer is 9216

 

Example 3:
362
 

Step 1:put down
 

Step 2:Multiply 2 with (3 + 1) = 8 and add 8 +1 = 9.put down 9.
 

Step 3:Multiply 3 with (3 + 1) = 12 put down 12
Answer is 1296

 

Example 4:
562
 

Step 1:put down 6
 

Step 2:Multiply 2 with (5 + 1) = 12 and add 12 +1 = 13.put down 3 and carry 1 .
 

Step 3:Multiply 5 with (5 + 1) = 30 + carry 1 = 31 put down 31
Answer is 3136