Find Square Root of Any Number in 5 Seconds - Mathematics Shortcuts and Tricks

Here is mathematical trick to find square root of any number without the help of pen/ pencil in few seconds. Shortcut tricks are very helpful for fast calculations in competitive exams as time allotted is too less for lengthy calculations. So shortcut tricks helps us to solve questions is very less time hence improving chances of getting good score and higher rank in merit.

Find Square Root of Any Number

Instructions:

Number must be a perfect square.
You must know squares of number from 1 to 9.

(1)² = 1; (2)² = 4; (3)² = 9; (4)² = 16 (5)² = 25 (6)² = 36 (7)² = 49 (8)² = 64; (9)² = 81;

Hence we know:

If last digit of a number is 1, last digit of its square root must be 1 or 9.
If last digit of a number is 4, last digit of its square root must be 2 or 8.
If last digit of a number is 5, last digit of its square root must be 5 only.
If last digit of a number is 6, last digit of its square root must be 4 or 6.
If last digit of a number is 9, last digit of its square root must be 3 or 7.

To find square root of any number follow steps below:

First split number into LHS and RHS. RHS = last two digits and LHS is other digits. (for eg in 1024, RHS = 24, LHS = 10)
Now take LHS and from the list of squares (1 to 9), take the square root of number just smaller than LHS. (Here LHS = 10. As 10 is just greater than 9 and less than 16 so we will pick square root of smaller number. (square root is 9 is 3).
This is our left side digit of answer. (Answer 1) = 3
Now last number of digit is 4 so last digit of square root must be 2 or 8.
Now multiply (Answer 1) with one higher digit and compare with LHS. ( 3 * 4 = 12 >10).
If LHS < answer, we will choose smaller number else bigger number. {as 10 < 12 we will choose 2 as last digit among 2 and 8}. (Answer 2) = 2
Now append (Answer 2) after (Answer 1) = 32. Final Answer.

Follow examples below to understand it better:

Eg. 1:

Find square root of 576
Step -1 => Here RHS = 76, LHS = 5
Step -2 => 5 is more than 4 but less than 9, so we will take square root of 4 = 2
Step -3 => (Answer 1) = 2. This is our left side digit of answer.
Step -4 => Now as last digit is 6, last digit of square root must be either 4 or 6.
Step -5 => Now 2 * 3 = 6 > 5. (multiplying (answer 1) by higher digit and comparing with LHS)
Step -6 => As 5 is less than 6 we will choose 4 as right hand side digit of answer (Answer 2). ( LHS < answer so smaller number).
Step -7 => Append (Answer 2) after (Answer 1) = 24

Hence square root of 576 is = 24. (Ans)

Eg. 2:

Find square root of 7744
Step -1 => Here RHS = 44, LHS = 77
Step -2 => 77 is more than 64 but less than 81, so we will take square root of 64 = 8
Step -3 => (Answer 1) = 8. This is our left side digit of answer.
Step -4 => Now as last digit is 4, last digit of square root must be either 2 or 8.
Step -5 => Now 8 * 9 = 72 < 77. (multiplying (answer 1) by higher digit and comparing with LHS)
Step -6 => As 77 is greater than 72 we will choose 8 as right hand side digit of answer (Answer 2). ( LHS < answer so smaller number).
Step -7 => Append (Answer 2) after (Answer 1) = 88

Hence square root of 7744 is = 88. (Ans)

To understand it better watch this video

Try square root of these numbers:

4096 =
3364 =
841 =
1681 =
5184 =

Mathematics is all about practice. Practice more and more problems of this type to improve your speed.

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