Success Khan Logo

Square and Cube

Objective type Questions, Notes for Govt Exams, current affairs, general knowledge, hindi objective questions, English objective questions, Mathematics objective Questions, Reasoning Objective Questions, study material for IBPS, study material for banks, study material for SSC, study material for DSSSB, Aptitude objective type Questions, Solved Question papers, Notes, Study Material, general knowledge questions and answers, gk questions and answers, hindi questions and answers, English questions and answers , mathematics questions and answers, reasoning questions and answers, current affairs questions and answers, general knowledge questions and answers for competitive Exams, gk questions and answers for competitive Exams, hindi questions and answers for competitive Exams, English questions and answers for competitive Exams, Mathematics questions and answers for competitive Exams, reasoning questions and answers for competitive Exams, current affairs questions and answers for competitive Exams, Railway jobs, banking job, corporate jobs, government jobs, govt jobs, private jobs, CPO, PCS, RRB, CDS, UPSC,Notes, Online Tests, practice sets, questions and answers with explanation for competitive examination, entrance test, Railway, IBPS, SSC, DSSSB, PCS, Banking for hindi, english, mathematics, reasoning, gk, current affairs and many more.

Introduction:

During the Mathematical Calculation , competitors are often required to remove classes and cubes of different numbers. Hence, the maximum practice of short-cut methods or tricks for competitors is very important. Therefore, it is advisable to use short-cut methods to remove the cube of greater than 50 numbers and larger than 20 numbers, but remembering square of numbers up to 50 and cube of numbers up to 20 Will be more lenient.


There are two methods for removing squares of different numbers and cubes.

(i) General Rate – This method allows the class and cubes of any number to be removed.
(ii) Special Rule –
This method extends the square or cube of any number following a particular condition.

 

(A) Remove square (TO FIND OUT SQUARE)

Normal method

TYPE-1 To the Square of two-digit numbers.

Trick → if AB is the number of two digits

(AB)2 = A2/2AB/B2

 

Example: (64)2 =?

Solution: (64)2 = 62 / 2 × 6 × 4 / 42 = 36 48,6 = 4096 Ans.

Note: Here 1 and 4 (From the right) are the numbers of the numbers obtained from 16 and 48, respectively.

 

TYPE-2 To find the square of three-digit numbers

TRICK → If ‘A B C’ is a number of three digits, then it can be sorted out as follows –

(ABC)2 = A2 /2.ab/2.ac + B2 /2.BC/ C2

 

Example: (346)2 =?

Solution: (346)2 = 32 / 2 × 3 × 4/2 × 3 × 6 + 42 / 2 × 4 × 6/62

Note: are 3, 4, 5 and 2 (Carry) numbers from 36, 48, 52 and 24, respectively.

 

Exercise Resolve by tricks –

1. (437)2 =?
2. (543)2 =?
3. (724)2 =?
4. (836)2 =?
5. (358)2 =?

 

TYPE-3 to find the square of four-digit numbers:

Trick → If ‘AB C D’ is a number of four digits, then it can be sorted out as follows

(ABCD)2 =?

1st step. = D2
2nd step. = 2.C.D
3rd step. = 2.B.D + C2
4th step. = 2.A.D + 2.B.C
5th step. = 2.A.C + B2
6th step. = 2.A.B
Last Step. = A2

 

Example: (6324)2 =?

Solution :
1st step.
= 42 = 16 ⇒ 16
2nd step. = (2 × 2 × 4) = 16 ⇒ 16
3rd step.
= (2 × 3 × 4) +22 = 28 ⇒ 28
4th step.
= (2 × 6 × 4) + (2 × 3 × 2) = 60 ⇒ 60
5th step.
= (2 × 6 × 2) + 32 = 33 ⇒ 33
6th step.
= (2 × 6 × 3) = 36 ⇒ 36
last step.
= 62 = 36

∴ ? = 363633281616 = 39992976 Ans.

Note: Here are numbers obtained from 1, 1, 2, 6, 3 and 3 (from the right) respectively 16, 16, 28, 60, 33 and 36

 

Exercise Solve them by TRICK-

1. (4567)2 =?
2. (8163)2 =?
3. (7435)2 =?
4. (3462)2 =?
5. (7246)2 =?

 

TYPE-4 To find the square of five-digit numbers

TRICK If ‘A B C D E’ is a number of five digits, then it can be sorted out as follows

(ABCDE)2 =?
1st step. = E2
2nd step. = (2 × D × E)
3rd step. = (2 × C × E) + D2
4th step. = (2 × B × E) + (2 × C × D)
5th step. = (2 × A × E) + (2 × B × D) + C2
6th step. = (2 × A × D) + (2 × B × C)
7th step. = (2 × A × C) + B2
8th step. = (2 × A × B)
last step. = A2

 

Example (32457)2 =?
Solution:
1st step. = 72 = 49 ⇒ 49
2nd step. = (2 × 5 × 7) = 70 ⇒ 70
3rd step.
= (2 × 4 × 7) + 52 = 81 ⇒ 81
4th step.
= (2 × 2 × 7) + (2 × 4 × 5) = 68 ⇒ 68
5th step.
= (2 × 3 × 7) + (2 × 2 × 5) + 42 = 78 ⇒ 78
6th step.
= (2 × 3 × 5) + (2 × 2 × 4) = 46 ⇒ 46
7th step.
= (2 × 3 × 4) = 22 = 28 ⇒ 28
8th step.
= (2 × 3 × 2) = 12 ⇒ 12
Last step.
= 32 = 9

∴ ? = 912284868817049 = 953456849 Answer.

Note: Here 4, 7, 8, 6, 7, 4, 2 and 1 (from the right) are obtained from 49, 70, 81, 68, 78, 46, 28 and 12 respectively. Has scores

 

Special Rule

To remove the square of any number made from a repeating number of the same number (To find the square of a repeat digit number)

TYPE-1 to find the square of 1 – repeated number.

In order to remove the square of numbers made from the repetition of the number 1, the number of times the number ‘1’ is in the number 1, 2, 3. in the increasing order from the right to the right. In decreasing order. The class of numbers given by typing 2, 1 is obtained.

Example 1. (111)2 = 12321 = 12321. Ans.
Example 2. (1111)2 = 1234321 = 1234321 Ans.
Example 3.
(11111)2 = 123454321 = 123454321 Ans.

 

Exercise Solve them by TRICK-

1. (11)2 =?
2. (111111)2 =?
3. (1111111)2 =?
4. (1111.111)2 =?
5. (111111.11)2 =?

 

TYPE-2. Find out the square of 2, 3, 4, 5, 6, 7, 8 or 9-repeated numbers.

If the number of numbers made from iterations of 2, 3, 4, 5, 6, 7, 8, or 9,

TRICK → the number of times the number of digits would be present in the answer number As much as 3,2,1 in the moving order and 1,2 in the descending order, on the right side, multiply it into the square of repeat digit and the number obtained on the right is multiplied. Adds it to the number on the left side. The product so obtained is the square of the answer number. So the square of repeat digit

Example 1. (222)2 = 22 × (12321) = 4 × (12321) = 49284 Answer
Example 2. (4444)2 = 42 × (1234321) = 16 × (1234321) = 19749136 Answer.
Example 3.
(777)2 = 72 × (12321) = 49 × (12321) = 603729 Answer.

 

Special tricks in case of 3, 6 or 9-repeat digit numbers

TRICK → With the help of ‘O Z E N’ , the square of the numbers formed from the iterative of the number 3 is drawn. Here Z (0) and N (9) are always kept constant i.e. once written and the number of O (1) and E (8) is presently known in the repeated scores, there is less one right than that

Example 1. (3333)2 = 11108889 Answer.
Note: Here there are four digits in 3333. Therefore, 1 and 8 have been written three or three times.

Example 2. (333.33)2 = 111108.8889 Answer.

 

TRICK → With the help of  ‘FO T FI S’ , the square of the numbers made from the recurrence of a score 6 is drawn. Here T (3) and S (6) always remain Constant. That is, once written and the number of times FO (4) and F1 (5) is in the number of times, in the number of repeat digit ‘6’, there is one less than that.

Example: (6666)2 = 44435556 Answer

Νοte: Here’s the four digits in 6666. Therefore 4 and 6 are written three times.

 

TRICK → With the help of ” NEZO , the square of the number made from the numerator 9 is always constant, i.e. written once. And the number of times N (9) and Z (0), repeat digit number 9, the number of times the presence occurs, is less than the right one.

Example 1. (999)2 = 998001. Answer.

Note: Here is the three digits in 999 Therefore 9 and 0 have been written twice

Example 2. (999.99)2 = 999980.0001 Answer

 

 

TYPE -3
To find out the square of numbers in the neighbourhood of 10, 100, 1000 and 10000

TRICK → To extract a square of 10, 100, 1,000 and 10,000 numbers, if the number to be extracted from the number of squares is less than one of these numbers, then the squared is written down on the left hand side of the number to be extracted is. And the number to be subtracted is written by the class on the right side.

Example 1 . (8)2 = 8 – 2/22 = 64 Answer.

Example 2 . (114)2 = 114 + 14 / (14)2 = 128196 = 12996 Answer.

Note: If the number of close numbers of 100 is to be removed, then the number to be subtracted and its two digits are kept on the right side.
Example 3.
(978)2 = 978 – 22 / (22)2 = 956/484 = 956484 Answer.

Example 4. (10032)2 = 10032 + 32/322 = 10064/1024 = 100641024 Answer.

 

Exercise Solve them by TRICK-

1. (87)2 =?
2. (124)2 =?
3. (972)2 =?
4. (1026)2 =?
5. (9982)2 =?
6. (9974)2 =?
7. (10023)2 =?
8. (10035)2 =?

 

Remember the class of these numbers to resolve quickly

 

(B) To find the cube

Simple Method

The two-digit numbers of the two digit numbers

TRICK Cube of a number of two digits is determined by the following
(i)
First, the digit of the two digits is cube of the number and placed on the left as the first position.
(ii)
The ratios are made in tens and unit digits.
(iii)
By dividing the first term with the ratio of tenth, multiplying the quotient divided by the ratio of the unit, the number received is placed on the right side of the first term as the second term. The third and fourth posts are also written by this type of action.
(iv)
Second and third posts are doubled and written down in them.
(v)
One digit is dropped on the right side and the remaining number is added to its left as a gain.

 

Example 1. (35)3 =?

Solution:
1st step.
= 33 = 27
2nd step. = 3 : 5
3rd step.
= 27 × 5 / 3 = 45
4th step.
= 45 × 5 / 3 = 75
5th step.
= 75 × 5 / 3 = 125
last step.
= (45 × 2) = 90 and (75 × 2) = 150

 

Example 2. (93)3 =?

Solution:
1st step.
= 93 = 729
2nd step. = 9 : 3 = 3 : 1
3rd step.
= 729 × 1 / 3 = 243
4th step.
= 243 × 1 / 3 = 81
5th step.
= 81 × 1 / 3 = 27
last step.
= (243 × 2) = 486 and (81 × 2) = 162

 

Exercise – Solve them by TRICK

1. (16)3 =?
2. (24)3 =?
3. (48)3 =?
4. (56)3 =?
5. (83)3 =?

 

Special Rules

To find out the cube of 1, 2, …… 9 repeated numbers.

TRICK Cube of a recurring number is obtained by multiplying that number into that square by that number.

 

Example 1 . (111)3 = (111)2 × 111 = 12321 × 111

= 1 / (1 + 2) / (1 + 2 + 3) / (2 + 3 + 2) / (3 + 2 + 1) / (2 + 1) / 1 = 1367631 Answer

 

Example 2. (222)3 = (222)2 × 222 = 49284 × 222

= 4 × 2 / (4 + 9) × 2 / (4 + 9 + 2) × 2 / (9 + 2 + 8) × 2 / (2 + 8 + 4) × 2 / (8 + 4) × 2 / 4 × 2

= 82630382848 = 10941048 Answer.

 

Exercise – Solve them by TRICK

1. (22)3 =?
2. (333)3 =?
3. (444)3 =?
4. (55)3 =?
5. (66)3 =?
6. (77)3 =?
7. (88)3 =?
8. (99)3 =?
9. (1111)3 =?

 

Remember the cube of these numbers for a quicker resolution

Objective type Questions, Notes for Govt Exams, current affairs, general knowledge, hindi objective questions, English objective questions, Mathematics objective Questions, Reasoning Objective Questions, study material for IBPS, study material for banks, study material for SSC, study material for DSSSB, Aptitude objective type Questions, Solved Question papers, Notes, Study Material, general knowledge questions and answers, gk questions and answers, hindi questions and answers, English questions and answers , mathematics questions and answers, reasoning questions and answers, current affairs questions and answers, general knowledge questions and answers for competitive Exams, gk questions and answers for competitive Exams, hindi questions and answers for competitive Exams, English questions and answers for competitive Exams, Mathematics questions and answers for competitive Exams, reasoning questions and answers for competitive Exams, current affairs questions and answers for competitive Exams, Railway jobs, banking job, corporate jobs, government jobs, govt jobs, private jobs, CPO, PCS, RRB, CDS, UPSC,Notes, Online Tests, practice sets, questions and answers with explanation for competitive examination, entrance test, Railway, IBPS, SSC, DSSSB, PCS, Banking for hindi, english, mathematics, reasoning, gk, current affairs and many more.





Average Practice Set – Mathematics
READ MORE

Average Practice Set – Mathematics

272

Average Practice Set – Mathematics
READ MORE

Average Practice Set – Mathematics

63

Average Practice Set – Mathematics
READ MORE

Average Practice Set – Mathematics

42

Average Practice Set – Mathematics
READ MORE

Average Practice Set – Mathematics

75

Average Practice Set – Mathematics
READ MORE

Average Practice Set – Mathematics

57

Number System Practice Set – Mathematics
READ MORE

Number System Practice Set – Mathematics

85

Search


Explore