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Very quick method to calculate square root and cube root of any number.

 Cube root


 If we remember the cube of numbers from 1 to 10, then we will be able to find the cube root of numbers up to 100000 very easy i.e. in few seconds.


 The cube of the numbers from 1 to 10 is:-


 1³ = 1

 2³ = 8

 3³ = 27

 4³ = 64

 5³ = 125

 6³ = 216

 7³ = 343

 8³ = 512

 9³ = 729

 10³ = 1000


 Q. 1.  Find the cube root of 97,336.

 Solution:- Unit digit -6

 Hence the unit digit of the required number is 6.

 ( 216= 6³)


 Now, 97  -----  (distinguish 336)

 The perfect cube number below 97 is 64 which is the cube of 4. Hence tens digit = 4

 Cube root of 97,336 = 46


 Q.2.  Find the cube root of 2744 .

 Solution:  2  744

 unit digit = 4

 cube number below 2 = 1

Cube root of 1 = 1

 ∴  1  4

 Ans: 14



 If the unit digit of the number is 8 then the unit digit of its cube root will be 2. And if the unit digit of the number is 2 then the unit digit of its cube root will be 8.


 8³ =  512  2³ = 8


 Q. What will be the cube root of 21,952?


 Solution:-

 1. The unit digit of the number is 2, so the unit digit of the cube root will be 8.

 2. Skip 952 and look for the whole cube number below 21 which is 8. (1,8,27,64,125 ..is the perfect cube number. See above)

 8  is the cube of ,  2.  Hence the tens digit is 2.

 Ans: 28


 // If the unit digit of the number is 3 then the unit digit of its cube root will be 7. And if the unit digit of the number is 7 then the unit digit of its cube root will be 3.


 //  If the unit digit of the number is 1,4,5,6,9,0 then the unit digit of its cube number also remains the same.

 

Q. Find the cube root of 912,673 .

 Solution:-  

912  673

729      7

9³         7

Ans: 97


 Q.  Find the cube root of 9261.

 Solution:- 

 9      261

8        1

2³       1

Ans: 21


 Q. What will be the cube root of 551,368 ?

 Solution:-

 551    368

512         2

8³            2

Ans: 82

Q. Find the cube root of 42,875.

Solution:-

 42    875

27         5

3³          5

Ans: 35


Q. What is the cube root of 17576?

Solution:-

17   576

8          6

2³        6

Ans: 26


 • Finding the Square Root of a Number


 Q.  Find the square root of 196.

 Solution:-

 1     96

 1      (4,6)

(1-1)

=0

0 is less than 1, so 4 will be unit digit.

 Ans: 14


 • First of all, separate two numbers up to the tens digit of the number.


 • Find the perfect square of the number less than the remaining numbers.  Here 96 is separated from 196 and the number left is 1.  A perfect square number less than or equal to 1 is 1.  Which is written below the remaining number 1.


 • Subtract the remaining number from the perfect square.(1-1)


 • Compare the remaining number with the square root of the perfect square number.  If the remaining number is bigger than square root number, take the unit digit of the larger number and if the square root number is smaller ,then take the smaller number.


 Ans: 14


Square root


 1²= 1       2² = 4

 3² = 9     4² = 16

 5² = 25   6² = 36

 7² = 49   8² = 64

 9²  = 81  10² =100

 • The unit digit of the number is 1, then the unit digit of the square root will be 1 or 9.


 • The unit digit of the number is 4, then the unit digit of the square root will be 8 or 2.


 • The unit digit of the number is 9, then the unit digit of the square root will be 3 or 7.


 • The unit digit of the number is 6  then the unit digit of the square root will be 6 or 4.



 Note:- 1. Tens digit:- In this method just like cube root, tens digit always after separating the number, the perfect square of the number less than the remaining number will be the square root of the number.



 Ex.  square root of 625 

 6      25

4-----2²

Hence tens digit of square root  =2


 Follow these steps to find the square root:-

 1.  Separates a number up to two numbers (ten digit) from the given number.


 2. Let's look at the perfect square number of the number less than the remaining number. The square root of this perfect square number will be the tens number.


 3. (Remaining Number - Whole square Number) = Remainder


 4.unit digit small number if


 remainder < square root


 The unit digit will take a larger number if


 remainder > square root



 Q. Find the square root of 5184.

 Solution:- 

51    84

49   (2,8)

51-49= 2

2 is less than 7(7²=49).

∴ we take 2 from (2,8) for unit digit.

Ans:- 72

 Note: 49,36,16,4 ---Perfect square number less than 51

 Q. Find the square root of 6084.

 Solution:-

60    84

49    (2,8)

(60-49)= 11

11 is more than 7(7²=49)

∴ unit digit of square root number= 8

Ans: 78

 Q. Find the square root of 15,129.

 Solution:-

151    29

144   (3,7)

(151-144)= 7

Remainder 7 is less than 12(12²= 144).

∴ unit digit of square root number= 3

Ans: 123


 Q. What will be the square root of 16129?

 Solution:-

161    29

144    ( 3,7)

(161-144)= 17

Here the remainder 17 is greater than 12(12²=144)

∴ unit digit of square root number= 7

Ans: 127



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