**1. (65)^2 = ? (square of 65?)**

**2. 12345 x 99999**

**3. 1234 x 11**

**4. √1444 = ?**

**5. 56^2**

**6. ∛205379**

**7. 343 x 999**

**8. 35^2**

**9. 23 x 27**

**10. 44^2**

**11. √3844**

**12. 32421 x 11**

**13. ∛39304**

**14. 74 x 76**

**15. 97 x 96**

**1. 65^2 =?**

**2. 12345 x 99999**

**3. 1234 x 11 = ?**

**4. √1444 = ?**

NUMBER |
SQUARE |
CUBE |
---|---|---|

1 |
1 |
1 |

2 |
4 |
8 |

3 |
9 |
27 |

4 |
16 |
64 |

5 |
25 |
125 |

6 |
36 |
216 |

7 |
49 |
343 |

8 |
64 |
512 |

9 |
81 |
729 |

10 |
100 |
1000 |

11 | 121 |
1331 |

12 | 144 |
1728 |

13 | 169 |
2107 |

14 | 196 |
2744 |

15 | 225 |
3375 |

16 | 256 |
4096 |

17 | 289 |
4913 |

18 | 324 |
5832 |

19 | 361 |
6859 |

20 | 400 |
8000 |

From the above table you will find squares are not ending with 2,3,7,8. But cubes are ending with 1,2,3,4,5,6,7,8,9.

We need to calculate square root of 1444.

Step 1: Split the number into two parts 14, 44 (last two digits are one part, remaining are one part); 44 is ending with 4 so the unit digit of square root ending with only 2 or 8.

2^2 = 4 ; 8^2 = 64 ;

Step 2: First part 14 is in between 3^2 to 4^2 (between 9 to 16)

so the second digit of square root is 3 or 4. In this case always you should take small number. Here small number is 3.

Step 3: We have found one digit is 3, what is the unit digit? (2 or 8). For this, take first part which is close to 3^2 to 4^2. It is close to 4^2 (16) only. so take 8 as second digit.

Step 4: Write first part answer(3) and second part answer(2) together.Hence Answer is 38.

**5. 56^2 = ?**

(50+6)^2;

Step 1: 50^2 = 2500 —-(1)

Step 1: 6 x 100 = 600 —-(2)

Step 1: 6^2 = 36 —-(3)

Add step 1,2,3 Answers = 2500+3600+36 = 3136

Answer is 3136.

**6. ∛205379**

NUMBER |
SQUARE |
CUBE |
---|---|---|

1 |
1 |
1 |

2 |
4 |
8 |

3 | 9 |
27 |

4 | 16 |
64 |

5 | 25 |
125 |

6 | 36 |
216 |

7 | 49 |
343 |

8 | 64 |
512 |

9 | 81 |
729 |

10 | 100 |
1000 |

11 | 121 |
1331 |

12 | 144 |
1728 |

13 | 169 |
2107 |

14 | 196 |
2744 |

15 | 225 |
3375 |

16 | 256 |
4096 |

17 | 289 |
4913 |

18 | 324 |
5832 |

19 | 361 |
6859 |

20 | 400 |
8000 |

We need to find cube root of 205379, see the above table

Step 1: Split the number into two parts 205, 379 (last three digits are one part, remaining are one part);

Note* : For square root calculations (we have splitted last two digits are one part, remaining are one part). for square and cube root we should know values from 1^2—— to 25^2,1^3—–to 10^3 are necessary.

379 is ending with 9 so the unit digit of cube root ending with only 9.

9^3 = 729 ;

Step 2: First part 205 is in between 5^3 to 6^3 (between 125 to 216)

so the second digit of square root is 5 or 6. In this case always you should take small number. Here small number is 5.

Step 3: We have found second digit 5, the unit digit is 9.

Step 4: Hence Answer is 59.

**7. 343 x 999 = ?**

343× 999 = ?

Step 1: For the above calculation you just minus 1 from the number then you will get 342.

Step 2: Subtract the 342 from 999, you will get 657.

Step 3: Finally write the both step 1,step 2 answers together.342657 is the answer.

343 × 999

Step 1: 343-1= 342

Step 2: 999-342=657

Step 3: 342657 (Answer)

NOTE: If no of 9’s are more than no of digits in number means just add 0’s infront of the number.(eg:00123× 99999).If no of digits in number is more than no of 9’s means dont use this technique.

**8. 35^2**

We need to calculate square for 35, The given number is ending with 5. So use this below shortcut (calculate square and number ending with 5)

Step 1: unit digit 5 x 5 = 25

Step 2: second digit 3 x (3+1) = 12

Ans : write step2 ans, step1 ans together = 1225

Step 1: 5 x 5 = 25

Step 2: 3 x (3+1) = 12

Step 3: Write the both step2,step1 answers together,

Ans = 1225

**9. 23 x 27 (Type 1) (Unit digit is different, second digit is same, sum of unit digit is 10)**

Step 1: second digit x (second digit + 1)

2 x (2+1) = 6 ;

Step 2 : Unit digit x Unit digit

3 x 7 = 21 ;

Step 3 : write both step 1 step 2 answers together,

Answer = 621.

**10. 44^2**

( 50 – 6 )^2

Step 1 : 50^2 = 2500

Step 2 : 6 x 100 = 600

Step 3 : 6^2 = 36

Step 4 : step 1 – step 2 + step 3 = 2500 – 600 + 36 = 1936.

Answer = 1936.

For Eg : 38^2

(50-12)^2

50^2 = 2500;

12×100 = 1200;

12^2 = 144

2500-1200+144 = 1444

**11. √3844**

We need to calculate square root of 3844.

Step 1: Split the number into two parts 38, 44 (last two digits are one part, remaining are one part); 44 is ending with 4 so the unit digit of square root ending with only 2 or 8.

2^2 = 4 ; 8^2 = 64 ;

Step 2: First part 38 is in between 6^2 to 7^2 (between 36 to 49)

so the second digit of square root is 6 or 7. In this case always you should take small number. Here small number is 6.

Step 3: We have found one digit is 6, what is the unit digit? (2 or 8). For this, take first part 38 which is close to 6^2 to 7^2. It is close to 6^2 (36) only. so take 6 as second digit.

Step 4: Write first part answer(3) and second part answer(2) together.Hence Answer is 62.

**12. 32421 x 11**

Step 1: Add 0 before and after the number 0324210

Step 2: add digits right to left 0+1=1, 1+2=3, 2+4=6, 4+2=6, 2+3=5, 3+0=3

Step 3: write the added result together from right 356631.

For Eg: 11 x 11

Step 1: 0110

Step 2: 0+1=1; 1+1=2; 1+0=1

Step 1: Ans = 121.

**13. ∛39304**

NUMBER |
SQUARE |
CUBE |
---|---|---|

1 |
1 |
1 |

2 |
4 |
8 |

3 |
9 |
27 |

4 |
16 |
64 |

5 |
25 |
125 |

6 |
36 |
216 |

7 |
49 |
343 |

8 |
64 |
512 |

9 |
81 |
729 |

10 |
100 |
1000 |

11 |
121 |
1331 |

12 |
144 |
1728 |

13 |
169 |
2107 |

14 |
196 |
2744 |

15 | 225 |
3375 |

16 | 256 |
4096 |

17 | 289 |
4913 |

18 | 324 |
5832 |

19 | 361 |
6859 |

20 | 400 |
8000 |

We need to find cube root of 39304, see the above table

Step 1: Split the number into two parts 39, 304 (last three digits are one part, remaining are one part);

Note* : For square root calculations (we have splitted last two digits are one part, remaining are one part). for square and cube root we should know values from 1^2—— to 25^2,1^3—–to 10^3 are necessary.

304 is ending with 4 so the unit digit of cube root ending with only 4.4^3 = 64 ;

Step 2: First part 39 is in between 3^3 to 4^3 (between 27 to 64) so the second digit of square root is 3 or 4. In this case always you should take small number. Here small number is 3.

Step 3: We have found second digit 3, the unit digit is 4.

Step 4: Hence Answer is 34.

**14. 74 x 76 (Type 1) (Unit digit is different, second digit is same, sum of unit digit is 10)**

Step 1: second digit x (second digit + 1)

7 x (7+1) = 56 ;

Step 2 : Unit digit x Unit digit

4 x 6 = 24 ;

Step 3 : write both step 1 step 2 answers together,

Answer = 5624.

**15. 97 x 96 **

Step 1 : (100-3) x (100-4)

Step 2 : (97 – 4 = 93) OR (96 – 3 = 93)

Step 3 : 3 x 4 = 12

Step 4 : write Step 2,Step 3 Answes together 9312.

Answer = 9312.