1. Squaring the Numbers By:Krishna Kumar Kumawat Maths Teacher

2. What is squaring? Squaringmeans that multiplying the term by itself. 3. Square of numbers whose unit digit is Zero ( 0 ) Just double the number of zeros at the rightside and write the square of the non-zeronumber in left. Example 1: 402= 1600 Example 2:7002= 490000 Example 3:21002= 4410000 Example 4:130002= 169000000 4. Square of numbers whose unit digit is 5. Write 25 in theright most place, then. Multiply the rest number with its successive numberand write in the leftExample 1: 252= 625 Example 2:652=4225 Example 3:852= 7225 Example 4:1152=13225 5. Square of numbers whose unit digit is 1. Writethe square of the previous numberandthen add the previous numberand the number whose square is being asked Example 1:212=202+ (20 + 21) =400 + 41=441 Example 2:812=802+ (80 + 81) =6400 + 161=6561 6. Square of numbers whose unit digit is 9. It is very similar to theprevious case. The difference is that here we have to subtract instead of addition. Example 1:392=402 ( 39 + 40 ) =1600- 79=1521 Example 2:1292=1302 ( 129 + 130 ) =16900- 259=16641 7. Square of numbers whose unit digit is 2. Writethe square of the base numberandthenmultiplythe sum oftheprevious numberand the number whose square is being asked, then add. Example 1:522=502+ 2( 50+ 52) =2500 + 204=2704Example 2:1122=1102+ 2( 110 + 112) =12100 + 44 4 =12544 8. Square of numbers whose unit digit is 8. Writethe square of the base numberandthenmultiplythe sum ofthebase numberand the number whose square is being asked by 2, then subtract it from the square of base number. Example 1:382=402- 2 ( 38 +40 ) =1600 - 156=1444 Example 1:582=602- 2 ( 58 +60 ) =3600-236=3364 9. Square of numbers whose unit digit is 3. Writethe square of the base numberandthenmultiplythe sum ofthebase numberand the number whose square is being asked by 3, then add it in the square of base number. Example 1:232=202+ 3 ( 20 +23 ) =400 + 129=529 Example 1:53 2=502+ 3 ( 50 +53 ) =2500-309 =2809 10. Square of numbers whose unit digit is 7. Writethe square of the base numberandthenmultiplythe sum ofthebase numberand the number whose square is being asked by 3, then subtract it from the square of base number. Example 1:472 =502- 3 ( 47 +50 ) =2500- 291 =2209 Example 1:372 =1402- 3 ( 137 +140 ) =19600-831 =18769 11. Square of numbers whose unit digit is 4. Writethe square of the base numberandthen subtract thesum of base numberand the number whose square is being askedfrom the square of the base number. Example 1:342=352 ( 34+ 35 ) =1225-69=1156 Example 2:542=552 ( 54 +55 ) =3025- 109=2916 12. Square of numbers whose unit digit is 6. Writethe square of the base numberandthen add the base numberand the number whose square is being asked Example 1:36 2=352+ (35+ 36) =1225 + 71 =1296 Example 2:762=752+ (75 + 76) =5625 +151 =5776 13. Important properties of squares 1.Thenumbers with unit digit0 , 1, 5or6always givethe same unit digit respectively, on squaring . 2.If the unit digit of any numberis 9 then the unit digit of the square of its number is always 1. 3.If the unit digit of anynumber is 2 or8 then the unit digitof the squareof its number is always 4. 14. Important properties of squares 4.If the unit digit of anynumber is 3 or7then the unit digitof the squareof its number is always 9.5.If the unit digit of anynumber is 4 or6 then the unit digitof the squareof its number is always6 .6.2, 3 7 and 8 never appear at unit digit in the square of a number. 15. Squaring the Numbers 16. Prepared by : Krishna Kumar Kumawat Maths Teacher C.F.D.A.V. Public School, Gadepan, Kota Rajasthan E-mail: kkk992840@yahoo.com Mob. 009928407883 17.