SQUARE AND SQUARE ROOT OF ANY NUMBER USING SIMPLE TRICK

OFTEN FINDING THE SQUARE/SQUARE ROOT OF THE NUMBER TAKES A LONG TIME, TIME MANAGEMENT IS MUCH ESSENTIAL IF YOU ARE APPEARING IN ANY COMPETITIVE EXAMINATION

HERE'S THE TRICK TO FIND THE SQUARE AND SQUARE ROOT OF THE NUMBERS IN EASY METHOD. YOU CAN SOLVE THE SQUARE OF ANY NUMBER WITHIN A SECONDS. YOU JUST NEED A LITTLE PRACTICE.

HERE WE GO.

1.     SQUARE OF THE NUMBER ENDING WITH 5.

FORMULA:   (n5)² = (n)*(n+1)(5²⁾

Example:

(i)                (25)² = (2)*(2+1)(5²)

        = 2*3(25)

        = 625

(ii)             (95²) = 9*10(25)

         = 9025

(iii)           (135²) = 13*14(25)

          = 18225

2.     SQUARE OF THE NUMBER NEAR 100.

                

Algorithm:

(i)                Find how much that number is less than 100.

(ii)             Find the square of the difference you got in step (i).

(iii)           Subtract the number (difference you got in step i ) from the number you are finding the square.

(iv)           Write the number which you got in step ii and iii, side by side.

Example:

(i)                (98²)

             100-92 =02; the number is two less from 100.

                                 Hence find the square of 2

                                   Sq. of 2 is 04 (*take it as 04)

                                   Now subtract 2 from 98  

                                   98-2=96

                                   Now write both the number side by side

                                   i.e 9604

                                   Hence sq. of 98 is 9602

(ii)             (92²)

Number is 8 less from 100, find the sq. of 8

Sq. of 8 is 64

Subtract 8 from 92, which is 84

Hence the sq. of 92 is 8464

NOTE: FOR NUMBER GREATER THAN 100, ADD THE DIFFERENCE TO THE NUMBER YOU ARE FINDING SQUARE OF.

Example:

 (108²) here the difference is 8, hence find sq. of 8, which is 64

Now add 108 with 8, which is 116, hence the sq. of 108 is 11664.

3.     FINDING THE ROOT OF IMPERFECT SQ. NUMBERS.

Formula :  root(n) = root(x) ± y/{2*root(x)}

Example:

 root(98)

Write 98 as 100-2

Where x=100 and y=2

Now use the formula

 root(98)= root(100)- 2/(2*root(100))

                = 10-2/(2*10)

                = 10-1/10

                = (100-1)/10

                = 99/10

                 = 9.9 (approx.)

Hence root of 98 is approx. 9.9

Similarly you can find for other numbers.