Maths - short cut tricks for square

In this post you learn some shortcut method related to square of number.here I will explain Some Tricks that improve your speed during calculation.

Trick 1: 2 Digit Number which ends in 5

Step 1: Multiply ten’s digit with its next number.
Step 2: Find square of unit’s digit. i.e.: Square of 5.
Step 3: Write answers of step 1 and step 2 to together or side by side.

Let’s take examples.  Find square of 45

Step 1:  =>    4 × ( 4 + 1 ) = 4 × 5 = 20
Step 2: = >   25  ( square of unit’s digit)
Step 3:  => (step 1) ( step 2)      Answer = 2025

Trick 2 : if you know square of the previous number.

Step 1: Find square of the previous number which is known.
Step 2: Multiply the number being squared by 2 and subtract 1.
Step 3: Add Step 1 and Step 2

Find square of 31.

Step 1 = > 30² = 900
Step 2 = >  (31 × 2) – 1 = 62 – 1 = 61
Step 3 = >  900 + 61 = 961

Trick 3 : Any two digit number square

Let’s say the number is two digit number. i.e. AB.
So B is units digit and A is tens digit.

Step 1: Find Square of B
Step 2: Find 2×A×B
Step 3: Find Square of A

Step 4 :Add carry from brackets right to left

Let’s take an example.

We want to find square of 37.

Step 1: Find square of 7.  Square of 7 = 49. So write 9 in the answer and 4 as carry to the second step.

Step 2: Find 2×(3×7)

        2 × (3 × 7) = 42.
42 + 4(Carry) = 46.

Step 3: Find square of 3

        Square of 3 = 9
9 + 4(Carry) = 13.
Write 13 in the answer.

        

        So the answer is 1369.

Basically in math form you can say

(n1n2)^2 = (n1)^2(2xn1xn2)(n2)^2

eg:
(42)^2 = (4)^2(2x4x2)(2)^2 = (16)(16)(4)

= > add carry from brackets right to left

 = (17)(6)(4) = 1764

Trick  4 : Square for number  From 31 to 50:

Find the square of 38.

Step 1 :  12 =50-38
Step 2 : Last 2 Digit :  Square of  12 = 144 =44 (1 Carry)
Step 3 : First 2 Digit:  25-12+1 =14

Final answer =1444 (First 2 Digit Last 2 Digit)
382=1444

Trick  5 : Square for number  From 51 to 80:

Find the Square of 62

Step 1 :  50+12 ( Yes, every time You have to think like this 50 + )
{If the number is 72 We will write 50+22}
Step 2 : Last 2 Digit : Square of 12 =144 = 44 ( 1 will be carry )
Step 3 : First 2 Digit : 25+12+1 =38
25 is constant number for every number 51-80 You have to add this!!
So our final result is 3844 (See First 2 Digit and Last 2 Digit above)
622 = 3844

Trick  6 : Square for number  From 81 to 100:

Find the square of 88

Step 1 : 88=100 -12 ( Yes 100-12 Only , not 50+38 or 80+8 )
{If the number is 92 then we have to think like 100-8}
Step 2 : Last 2 Digit : 122 = 144 = 44 (1 carry )
Step 3 : First 2 Digit : 88 - 12 + 1 =77

So our final Answer is 7744 (First 2 Digit Last 2 Digit)