Square tricks and tips of Natural numbers (301 - 399) for competitive exams

Now I am going to guide you for faster calculation of square with the help of some tricks. If you have prepared the procedure/ trick for the square of natural numbers from 25 to 300 then this tricky method of calculation of square of numbers more than 300 will help you to save your precious time in calculation,


Let's see this trick and practice it for fastest calculation. 

In this range we use the trick which uses 300 & the number itself

Method :-

Step 1^st :- Subtract 300 from the numbers  & get the difference.

Step 2^nd :- Now add the above difference in the number  & get the result.

Step 3^rd :- Now multiply above result by 3 to get the product.

Step 4^th :- Now follow the above product with the square of the difference of 1^st step in 2- digit only.

Demonstration of above method:-

301² →   Step 1^st    301 – 300 = 01

               Step 2^nd   301 + 01 = 302

               Step 3^rd   302 × 03 = 906

               Step 4^th    Arrange it like this 906(01)² → 90601

Get the required answer 301² = 90601

302² →   Step 1^st    302 – 300 = 02

                Step 2^nd   302 + 02 = 304

                Step 3^rd   304 × 03 = 912

                Step 4^th    Arrange it like this 912(02)² → 91204

Get the required answer 302² = 91204

303² →   Step 1^st    303 – 300 = 03

                Step 2^nd   303 + 03 = 306

                Step 3^rd   306 × 03 = 918

                Step 4^th  Arrange it like this 918(03)² → 91809

Get the required answer 303² = 91809

304² →   Step 1^st    304 – 300 = 04

                Step 2^nd   304 + 04 = 308

                Step 3^rd   308 × 03 = 924  

                Step 4^th  Arrange it like this 924(04)² → 92416

Get the required answer 304² = 92416

306² →   Step 1^st    306 – 300 = 06

                Step 2^nd   306 + 06 = 312

                Step 3^rd   312 × 03 = 936              

                Step 4^th   Arrange it like this 936(06)² → 93636

Get the required answer 306² = 93636

307² →   Step 1^st    307 – 300 = 07

                Step 2^nd   307 + 07 = 314

                Step 3^rd   314 × 03 = 942

                Step 4^th   Arrange it like this 942(07)² → 94249

Get the required answer 307² = 94249

308² →   Step 1^st    308 – 300 = 08

                Step 2^nd   308 +  08 = 316

                Step 3^rd   316 × 03 = 948

                Step 4^th   Arrange it like this 948(08)² → 94864

Get the required answer 308² = 94864

309² →   Step 1^st    309 – 300 = 09

                Step 2^nd   309 + 09 = 318

                Step 3^rd   318 × 03 = 954

                Step 4^th   Arrange it like this 954(09)² → 95481

Get the required answer 309² = 95481

211² →   Step 1^st    311 – 300 = 11

                Step 2^nd   311 + 11 = 222

                Step 3^rd   322 × 03 = 966

                Step 4^th   Arrange it like this 966(11)² →966(121) → 96 (6+1) 21 →96721

Get the required answer 311² = 96721

312² →      Step 1^st    312 – 300 = 12

                  Step 2^nd   312 + 12 = 324

                  Step 3^rd   324 × 03 = 972

                  Step 4^th  Arrange it like this 972(12)² → 972(144) → 97(2+1) 44 →97344

Get the required answer 312² = 97344

313² →   Step 1^st    313 – 300 = 13

                Step 2^nd   313 + 13 = 326

                Step 3^rd   326 × 03 = 978

                Step 4^th   Arrange it like this 978(13)² → 978(169) →97 (8+1) 69 →97969

Get the required answer 313² = 97969

314² →   Step 1^st    314 – 300 = 14

                Step 2^nd   314 + 14 = 328

                Step 3^rd   328 × 03 = 984

                Step 4^th   Arrange it like this 984(14)² → 984(196) →98 (4+1) 96 →98596

Get the required answer 314² = 98596

326² →   Step 1^st    326 – 300 = 26

                Step 2^nd   326 + 26 = 352

                Step 3^rd   352 × 03 = 1056

                Step 4^th    Arrange it like this 1056(26)² → 1056(676) →10(56+6) 76 →106276

Get the required answer 326² = 106276

336² →   Step 1^st    336 – 300 = 36

                Step 2^nd   336 + 36 = 372

                Step 3^rd   372 × 03 = 1116

                Step 4^th  Arrange it like this 1116(36)² → 1116(1296) →11(16+12) 96 →112896

Get the required answer 336² = 112896

349² →   Step 1^st    349 – 300 = 49

                Step 2^nd   349 + 49 = 398

                   Step 3^rd   398 × 03 = 1194

                   Step 4^th   Arrange it like this 1194(49)² → 1194(2401) →   1(194+24) 01 → 121801

Get the required answer 349² = 121801

354² →   Step 1^st    354 – 300 = 54

                Step 2^nd   354 + 54 = 408

                Step 3^rd   408 × 03= 1224

                Step 4^th   Arrange it like this 1224(54)² → 1224(2916) →12(24 + 29) 16 →125316

Get the required answer 354² = 125316

386² →   Step 1^st    386 – 300 = 86

               Step 2^nd   386 + 86 = 472

               Step 3^rd   472 × 03 = 1416

               Step 4^th   Arrange it like this 1416(86)² → 1416(7396) → 14(16+73)96 →148996

Get the required answer 386² = 148996

399² →   Step 1^st    399 – 300 = 99

                Step 2^nd   399 + 99 = 498

                Step 3^rd   498 × 03 = 1494

                Step 4^th   Arrange it like this 1494(99)² → 1494(9801) → 1(494+98) 01 → 159201

Get the required answer 399² = 159201

To be continued like this upto 399 only (this trick is valid for 301 to 399)