Today we will discuss the tricks to find out square roots and cube roots of numbers.

Before learning the trick to solve the square roots and cube roots. One must remember the squares up to 30 and cubes up to 15 (at least).

#### TRICKS TO FIND SQUARE ROOTS

**Squares from 1 to 30**

1 | 1 |

2 | |

3 | 9 |

4 | 16 |

5 | 25 |

6 | 36 |

7 | 49 |

8 | 64 |

9 | 81 |

10 | 100 |

11 | 121 |

12 | 144 |

13 | 169 |

14 | 196 |

15 | 225 |

16 | 256 |

17 | 289 |

18 | 324 |

19 | 361 |

20 | 400 |

21 | 441 |

22 | 484 |

23 | 529 |

24 | 576 |

25 | 625 |

26 | 676 |

27 | 729 |

28 | 784 |

29 | 841 |

30 | 900 |

### Trick to find Perfect Square Roots

Learn above squares before applying this trick.

Now lets observe the pattern of the squares from 1 to 9.

IF NUMBER END WITH | SQUARES END WITH |

4 | 2/8 |

9 | 3/7 |

6 | 4/6 |

5 | 5 |

1 | 1/9 |

Keeping in mind the above pattern, now see how we can find the square of numbers.

**Example: _/2304 = ?**

Solution - First see the last two digits of the number of which we have to find the square root.

Here the last two digits of the number are 04. So we can see from the above table that square root will end with either 2 or 8.

Cross the last two digits after this step.

Now check the remaining number. Here the remaining number is 23. Take the perfect square less than this number i.e. before 23. We all know that 16 is the perfect square less than 23 and 16 is the square of 4. So 4 will be the first number of square root of 2304.

Now the question arises whether 42 will be the square root or 48.

There are two ways to identify this:

Take the range in which the options are coming

Here the range is 40-50

40^2 = 1600

50^2 = 2500

2304 is near to 2500,

So 48 will be the answer.

45^2 = 2025

2304 > 2025

So, number more than 45 will be the answer, So 48 will be the answer.

Range in which the given number lies.

Difference of number and lowest range,

There are two ways to identify this:

__1st Way__Take the range in which the options are coming

Here the range is 40-50

40^2 = 1600

50^2 = 2500

2304 is near to 2500,

So 48 will be the answer.

__2nd Way__**Take the square of the number (common value) which ends with 5 ( as it is easy to find squares of number ending wit 5 ) and lies between 42 and 48 i.e. take square of 45.**

45^2 = 2025

2304 > 2025

So, number more than 45 will be the answer, So 48 will be the answer.

**ANSWER = 48**

**Trick to find Imperfect Square**

Generally Approximation questions contains imperfect squares in their questions. So lets discuss the tricks to solve the imperfect squares.

**EXAMPLE: _/ 9000****Consider the range in which the given number lies. Then take the difference from the lowest number of the range.Divide the resultant number with the number of lowest range multiplied by 2.Add both results and that will be the answer.**

Range in which the given number lies.

**90 will be surely part of answer as square of 90 is 8100 which is less than 9000. Now take the difference as numerator and divide it by the other part i.e. 90*2 (Always multiply the denominator by 2)**

#### TRICK TO FIND CUBE ROOTS

Cubes from 1 to 15

1 | 1 |

2 | 8 |

3 | 27 |

4 | 64 |

5 | 125 |

6 | 216 |

7 | 343 |

8 | 512 |

9 | 729 |

10 | 1000 |

11 | 1331 |

12 | 1728 |

13 | 2197 |

14 | 2744 |

15 | 3375 |

Now, observe the pattern of the cubes from 1 to 9.

### TRICK TO FIND PERFECT CUBE ROOTS

**EXAMPLE: _3/17576**

First see the last three digits of the number of which we have to find the cube root.

Here the last three digits of the number are 576. So we can see from the above table that cube root will end with 6.

Here the last three digits of the number are 576. So we can see from the above table that cube root will end with 6.

Cross the last digits of the number after this step.

Now check the remaining number i.e. 17. Perfect cube before 17 is 8 and 8 is cube of 2. So 2 will be the first digit of cube root.

**ANSWER = 26**

### TRICKS TO FIND IMPERFECT CUBES

Generally Approximation questions contains imperfect cubes in their questions. So lets discuss the tricks to solve the imperfect cubes.

**EXAMPLE: _3/80000**

Consider the range in which the given number lies. Then take the difference of the lowest number of the range and given number.

The range in which 8000 lies is 40^3 - 50^3

Always multiply the result with 10

= 40 + 2.5

= 42.5 ( approx)

= 40 + 2.5

= 42.5 ( approx)

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