[Tutorial 3]Apitude Tricks for fast mental Calculation | Maths speed calculation tricks for competitive Exams

Squaring of any two digit number within fraction of seconds(Note its only for 2 digit numbers)

We already shared Part 2/[Tutorial 2 click here to go] Maths Tricks|Aptitude Tricks|Speed Maths|Fast Calculation|mental maths tricks,maths. So in this Tutorial 3 we gonna share maths tricks and shortcut key to do fast mental calculation for squaring 2 digit number.This will be very useful for competitive exam.keep practice more problem based on this

Square of any 2 digit number by using simple steps to get solutions in easy way without taking even 5 seconds

Method 1 :Note:Below examples are near to 50 square numbers

Question 1: Square of 10 or 10^2 

Answer: 100 its easy to get solution but see next question

Question 2: Square of 47 or 47^2 
Answer:
Rule :1
step 1:check the number is near to 50 if yes
step 2: 50-47=3

           Now subtract (50-47 difference) i.e 3 from   25  we get 25-3= 22

Step 3: Now  Square that difference number (50-47 difference) i.e 3

             We get 09 

Step 4: solution 47^2=(25-3)3^2

              Ans:=:2209

Question 3: 42^2 =(25-8)8^2

                Ans=  1764

Question 4: 56^2 = (25+6)6^2

                 Ans=  3136 

 Question 5: 65^2 = (25+15)15^2

                Ans =

                           step 1: (40)15^2  

                           Step 2: 40(225) make that as four digit i.e assume 40(00)+225 =4225

Method 2 , Note:Below examples are near to 100 square numbers

Example 1: 92^2 =(92-8)8^2

                Ans=  (84)8^2

                Solution is ----- = 8464

Example 2: 96^2 =(96-4)4^2

                Ans=  (92)4^2

                Solution is ----- = 9216

Example 3: 84^2 =(84-16)16^2

                Ans=  (68)16^2

                           (68)256      ---> 6(8+2)56 {{make that as four digit i.e assume68(00)+256}}

                Solution is ----- = 7056

Example 4: 104^2 =(104+4)4^2

                Ans=  (108)4^2

                           (108)16      ---> 10816 {{make that as five digit i.e assume108(00)+16}}

                Solution is ----- = 10816

Example 5: 112^2=(112+12)12^2

                  Ans: (124)12^2  ---> (124)144 {{make that as five digit i.e assume124(00)+144}}

 Solution is ----- = 12544

Most common method/trick for solving all two digit numbers from 1 to 100 square in our head or without calculator

 Example a:  67^2 ==== [6^2]...[7^2]+20*6*7=[3649]+840...... i.e [3649]+840= 4489

 Example b:  25^2====[2^2]....[5^2]+20*2*5=[0425]+200......i,e., 625

 Example c:   74^2====[7^2]....[4^2]+20*7*4=[4916]+560.......i.e., 5476

                    

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[Maths Tricks]Fast calculation in maths tricks tutorial 2

We already shared Part 1/[Tutorial 1 click here to go] Maths Tricks|Aptitude Tricks|Speed Maths|Fast Calculation|mental maths tricks,maths. So in this Tutorial 2 we gonna share maths tricks and shortcut key to do fast mental calculation here.

 

 

How to find calculate remainder on dividing by 27 and 37 in 3 secs

Question 1:  find the remainder  45286789 on dividing by 27 and 37 repectively
Answer:
Rule :1
step 1:split that  45286789 as 45.... 286....789
step 2:Some all digits above separated digits ---> 45+286+789= 1120
           Again split  1120 as 1...120
           Add above separated digits --> 1+120 = 121(Repeat the step 2 until get as 3 digit number)
Step 3: Now divide 121 by 27 we get remainder as 121/27 = 4 as Q(quotient) ; 13 as Remainder (108+13=121)
            Now divide 121 by 37 we get remainder as 121/37 = 3 as Quotient ; 10 as Remainder
(111+10=121)  

verification/Proof
 45286789/27 =1677288 as Q  ; 13 as remainder  ( 45286776  + 13 =45286789)
 45286789/37 =1223967 as Q  ; 10 as remainder   ( 45286779 + 10 =45286789)

Tricks to find remainder easily by dividing 27 and 37

Question 2:  find the remainder  34568278 on dividing by 27 and 37 repectively
Answer:
Rule :1
step 1:split that  45286789 as 34.... 568....278
step 2:Some all digits above separated digits ---> 34+568+278= 880
           now no need to split  880 because we got the number as three digit
           Add above separated digits --> 0+880 = 880 only
Step 3: Now divide 880 by 27 we get remainder as 880/27 = 32 as Q(quotient) ; 16 as Remainder (864+16=880)
            Now divide 121 by 37 we get remainder as 121/37 = 23 as Q(quotient) ; 29 as Remainder
(851+29=880)  

verification/Proof
 34568278 /27 =1280306 as Q  ; 13 as remainder  ( 34568262 + 16=34568278 )
 34568278 /37 = 934277  as Q  ; 29 as remainder  ( 34568249 + 29 =34568278 )

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