Fast and Easy Method to Take Square Root- Math Tricks

Fast and Easy Method to Take Square Root- Math Tricks:

Fast and Easy Method to Take Square Root is given here, candidates those who are preparing for banking and all other competitive exams can use this trick in the examination to save time. 

POINTS TO REMEMBER:

·         When 2² = 4, then √4 = 2

·         Here 4 is the square of 2

·         2 is the square root of 4

·         A Square of a number can never end with 2, 3, 7 and 8

Table 1:

One’s digit of a square	One’s digit of the square root
1	1 or 9
4	2 or 8
5	5
6	4 or 6
9	7 or 3

To find the square of a number which is a multiple of ‘5’

25² = [2×3] 5²

= [6] 25 = 625

i.e., AB² where B=5

AB² = [A× next number] B²

For example, 85² = [8×9] 25 = 7225

115² = [11×12] 25 = 13225

155² = [15×16] 25 = 24025

This method can be followed for all numbers divisible by 5

TYPE 1:

To find the square root of a 3-digit number

EXAMPLE: √841

STEP 1: Consider the one’s digit of the given number i.e., 1

From Table 1, if the one’s digit of the square is ‘1’ then the square root would either end with ‘1’ or ‘9’

STEP 2: Always ignore the ten’s digit of the given number

STEP 3: Now the remaining number other than the one’s and the ten’s digit in the given number is ‘8’

Consider a square-root of a square which is nearer to as well as lesser than ‘8’.

Here it is ‘4’ which is nearer to as well as lesser than ‘8’. Hence the square root of 4 i.e., ‘2’ is taken

STEP 4: we already know the one’s digit of the square root to be either 1 or 9 from STEP 1

Therefore the square root of ‘841’ lies between 21 and 29

STEP 5:

Take a number divisible by ‘5’ between 21 and 29, that is ‘25’

25² = [2×3] 25 = 625

Now 625 < 841

25² is itself lesser than 841. Then 21² will be much lesser than 841.

Therefore, the remaining option is ‘29’

√841 = 29

TYPE 2:

To find the square root of a 4-digit number

EXAMPLE: √8464

STEP 1: Consider the one’s digit of the given number i.e., 4

From Table 1, if the one’s digit of the square is ‘4’ then the square root would either end with ‘2’ or ‘8’

STEP 2: Always ignore the ten’s digit of the given number

STEP 3: Now the remaining numbers other than the one’s and the ten’s digit in the given number is‘84’

Consider a square-root of a square which is nearer to as well as lesser than ‘84’.

Here it is ‘81’ which is nearer to as well as lesser than ‘84’. Hence the square root of 81 i.e., ‘9’ is taken

STEP 4: we already know the one’s digit of the square root to be either 2 or 8 from STEP 1

Therefore the square root of ‘8464’ lies between 92 and 98

STEP 5:

Take a number divisible by ‘5’ between 92 and 98, that is ‘95’

95² = [9×10] 25 = 9025

Now 9025 > 8464

95² is itself greater than 8464. Then 98² will be much greater than 8464

Therefore, the remaining option is ‘92’

√8464 = 92

TYPE 4:

To find the square root of a 5-digit number

EXAMPLE: √18769

STEP 1: Consider the one’s digit of the given number i.e., 9

From Table 1, if the one’s digit of the square is ‘9’ then the square root would either end with ‘3’ or ‘7’

STEP 2: Always ignore the ten’s digit of the given number

STEP 3: Now the remaining numbers other than the one’s and the ten’s digit in the given number is‘187’

Consider a square-root of a square which is nearer to as well as lesser than ‘187’

Here it is ‘169’ which is nearer to as well as lesser than 187. Hence the square root of 169 i.e., ‘13’ is taken

STEP 4: we already know the one’s digit of the square root to be either 3 or 7 from STEP 1

Therefore the square root of ‘18769’ lies between 133 and 137

STEP 5:

Take a number divisible by ‘5’ between 133 and 137, that is ‘135’

135² = [13×14] 25 = 18225

Now 18225 < 18769

135² is itself smaller than 18769. Then 133² will be much lesser than 18769

Therefore, the remaining option is ‘137’

√18769 = 137

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