Maths shortcut to find unit digit of an exponent

Maths shortcut for finding units digit with exponent of base 3 and 7 are given in this post .Now u can solve a problem that is asked to find the units digits of given number with its units digit either 3 or 7.This amazing shortcut will cut your time in calculating the answer.If you are preparing for any competitive exam then this trick will help you most.Lets go straightly into knowing the trick with out wasting any time.Here i am going to assume a number with its units digit 3 as follows.

ASSUMED NUMBER IS (563)^155.Now you have to find the units digit for the number with exponent 155.It will be a tough ask when you don’t know this trick while calculating the answer.

Maths shortcut finding units digit of any exponent that ends with base 3 :

1.We have to find the units digit for the expression (563)^155 ?

  • For finding the units digit of the above expression first of all we need to know the units digit for the power of 3 and they can be given as follows.
  • (3^1=3) , (3^2=9) , (3^3=27) , (3^4=81) , (3^5=243) , (3^6=729) , and so on ………
  • In the above step if you check the units digit they will be getting repeated after every four successful calculations.There will be a cyclicity of 4 for every unit digit to get repeated again.We need to remember the units digit 3,9,7,1.
  • From the above given expression,155 is the exponent of base 3.Now we need to divide it by 4 ( as the cyclicity from the above step).The remainder will be 3.From the above step,we get 7 as the units digit.
  • If the remainder is 1 then we need to take units digit as 3,if 2 then 9,if three then 7 and if the remainder is 0 then the units digit will be 1.Remember this point.Its important.
  • Thus we calculate the units digit even if there is a large number present in the form of an exponent to a number with its unit digit as 3.

For more details regarding this math shortcut u can watch the video

In the same way you can calculate the unit digit of an exponent with its base as 7 the video of the same can be given as follows.

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Fastest way to find Multiplication of two numbers

Well guys we are going to teach you the Fastest way to find Multiplication of two numbers your teacher had not taught you while schooling.With this method you can find the product of two numbers in just a min instantly and on practice you can find the product you can find in 10 secs.Isn’t it coo! So lets get in to the procedure.Take an example of finding the product of 97 and 105.

Procedure to find the product of 97 x 105 ?

  • Take the nearest base of two numbers – the nearest base is 100 for those two numbers.
  •  Write down the difference between the base and the two numbers i.e., 97-100 = -3 and 105-100=5.
  • Add the difference values in opposite numbers we get 97+5 = 102 and 105-3 = 102.
  • Now we will get a common value for both and just mulitply the base with the value i.e., 100 x 102 = 10200
  • Mulitply the two difference values which we have obtained in step 2 .We get -3×5=-15 and add it to product generated in the above step.i.e, 10200 + (-15) = 10185.
  • That’s it the product of the two values 97 x 105 = 10185.

If you could not get what we have written here then watch the video demonstration here ans subscribe on our channel for more amazing tricks.

Find square root of a number in 5 seconds?

Well guys here we are going to post an aptitude trick on how to find square root of a number in 5 seconds.Lets begin the trick . Before starting you should know the following,Some people may know it but still i am posting it here

  • square of 2 = 4
  • square of 3 = 9
  • square of 4 =16
  • square of 5 = 25
  • square of 6 = 36
  • square of 7 = 49
  • square of 8 = 64
  • square of 9 = 81

All you need is to just remember the unit digit number in the squares of above all numbers.So if square root of any three or four digit number will be asked then divide the number into two parts i.e.., (wx,yz)and then check the units digit of the number. For example consider some numbers

PART-1

  • 625    – (25) unit digit is 5 so the square root of 625 will end up containing 5 in the units digit.
  • 729    – (29) unit digit is 9 so the square root of 729 will end up containing 3 or 7 in the units digit.
  • 1156  – (56) unit digit is 6 so the square root of 1156 will end up containing 4 or 6 in the units digit.
  • 2304 – (04) unit digit is 9 so the square root of 2304 will end up containing 2 or 8 in the units digit.

Now in part 1 we know the units digit and in second we are going to know the exact squares of above given number

PART-2

  • 6 is remained in the second part so find the lowest square below 6 we get 4 and the square root of 4 is 2, then square root of 625 will be 25.
  • 7 is remained in the second part so find the lowest square below 7 we get 4 and the square root of 4 is 2, then square root  will be 23 or 27.
  • 11 is remained in the second part so find the lowest square below 11,we get 9 and the square root of 9 is 3,then square root will be 34 or 36.
  • 23 is remained in the second part so find the lowest square below 23,we get 16 and the square root of 16 is 4,then square root will be 42 or 48.

Thus we can find the square root of any three digit or four digit number in 5 seconds.If any body have doubts or query then do please comment below.Thank you.