Square Root & Cube Root

                                          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

1. 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.
2. 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:

1. Cube of a 2-digit 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.
2. This trick works only for perfect cubes, it will not work for any arbitrary 6-digit
3. It works only for integers

Example: 

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)

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.

Step 4:
Combining the results we get the answer as 55.

(166375)^1/3 = 55