Square
Root and Cube Root
Shortcut Trick use for Perfect Square Root or Cube Root
Number

Square

Last Digit of its Square Root

Cube

Last Digit of its Cube Root

1

1

1

1

1

2

4

4

8

8

3

9

9

27

7

4

16

6

64

4

5

25

5

125

5

6

36

6

216

6

7

49

9

343

3

8

64

4

512

2

9

81

1

729

9

10

100

0

1000

0

Observation
1.If the unit
digit of any number is 2 or 8 then its square will have
unit digit as 4.
2.If the unit
digit of any number is 3 or 7 then its square will have
unit digit as 9.
3.If the unit
digit of any number is 4 or 6 then its square will have
unit digit as 6.
4.If the unit
digit of any number is 1 or 9 then its square will have
unit digit as 1.
5.If the unit
digit of any number is 0 then its square will have unit
digit as 0.
Example
1.Find the square
root of 529
5,29(Last two digit)
3..............9
7..............9
3/7
5
5 is between 2 & 3
So value is 2
2 * 3=6
As compare 5 with 6 ,So
5 is less than 6 so value of unit is 3(i.e Smaller)
Now, Square Root of 529
is 23
2.Find the square
root of 6084
60,84(Last two digit)
2..............4
8..............4
2/8
60
60 is between 49 &
64
So value is 7
7 * 8=56
As compare 56 with 60
,So 60 is large than 56 so value of unit is 8(i.e Larger unit digit)
Now, Square Root of 529
is 78
Square Root
 First Find the last digit of the square root ,which can directly be obtained by looking the last digit of the number and then referring the table.
 Next,Ignore the last 2 digits of the number and look at the number which remain. Think of a number ,whose square is just equal or less then this remaining number.
Ex:Find
the Square Root of 10 24.
Last Digit
of 1024 is 4
According
to Above Table
2........................................................4
8........................................................4
Ignore
the Last two digit that is 24
Now
Focus on 10
Now
find the square of number which is equal or lesser than 10.
3^2=9
4^2=16
From
here we find square of 3 is less than to 10.
So,This
is the ten's digit of square root is 3
Now
9 (Smaller than 10 ,so we will choose small digit i.e. 2)
is less than 10 that why unit digit is 2.
Now
,Answer of square root of
1024 is 32.
Cube
Root
This
technique helps you find out the cube root of a 4 or 5 or 6 digits
number mentally.
Note:
Note:
 Cube of a 2digit number will have at max 6 digits (88^3 = 681,472). That implies if you are given with a 6 digit number, its cube root will have 2 digits.
 This trick works only for perfect cubes, it will not work for any arbitrary 6digit
 It works only for integers
Say
you have to find the cube root of 166375. It is
known that it’s a perfect cube.
Step
1:
Now
divide this number into two parts. The right hand side
should always have 3 digits. Remaining digits will
come in left hand side. Do it as shown below.
166.........................................375
You know the answer will have 2 digits. Digit at tens place and digit at units place. We will get the digit at tens place using the left hand side of the original number (166) and digit at units place using right hand side of the number (375)
come in left hand side. Do it as shown below.
166.........................................375
You know the answer will have 2 digits. Digit at tens place and digit at units place. We will get the digit at tens place using the left hand side of the original number (166) and digit at units place using right hand side of the number (375)
Step
2.
For left hand side we need to use Above Table . We have to see the above table in which 166 lies between 125 and 216. So we will take the cube root of the smaller number i.e. 125 which is 5.
So 5 is the tens digit of the answer.
Step 3.
For right hand side we need to use Above Table. Since our original number (the perfect cube) ends in 5 (see 166375), its cube root will ends in 5.
Thus the units digit will be 5.
For left hand side we need to use Above Table . We have to see the above table in which 166 lies between 125 and 216. So we will take the cube root of the smaller number i.e. 125 which is 5.
So 5 is the tens digit of the answer.
Step 3.
For right hand side we need to use Above Table. Since our original number (the perfect cube) ends in 5 (see 166375), its cube root will ends in 5.
Thus the units digit will be 5.
Step
4:
Combining the results we get the answer as 55.
Combining the results we get the answer as 55.
(166375)^1/3 = 55
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