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GxmUl

GxmUl. jmwq – ATvIN iqAwr krqw:- ivSw – 2 krmjIq s.h.s Bum`dI. audyS. ies pRojYkt dw audyS ividAwrQIAw nUM GxmUl bwry jwxU krwauxw hY [. GxmUl. jykr iek sMiKAw m dw Gx = n hovy qW n dw GxmUl m hovygw[. audwhrx. ijvyN: 2 dw Gx =2 3 =8 hY 3 √ 8 = 2 hovygw[

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GxmUl

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  1. GxmUl jmwq – ATvIN iqAwr krqw:- ivSw – 2 krmjIq s.h.s Bum`dI

  2. audyS • ies pRojYkt dw audyS ividAwrQIAw nUM GxmUl bwry jwxU krwauxw hY [

  3. GxmUl jykr iek sMiKAw m dw Gx = n hovy qW n dw GxmUl m hovygw[

  4. audwhrx ijvyN: 2 dw Gx =23 =8 hY 3√8 = 2 hovygw[ 5 dw Gx =53 = 125 hY 3√125 = 5 hovygw[

  5. GxmUl dw inSwn jW icMn 3√ ijvyN ik vrgmUl ivc √ dw inSwn vrqdy hW, iesy qrW GxmUl ivc 3√ dw inSwn vrqWgy[

  6. audwhrx: GxmUl dy inSwn ivc AMk 3 dw Akwr ilKI sMiKAw dy Awkwr qoN kwPI Cotw hoxw cwhIdw hY[ ijvyN ik 15 dw GxmUl ilKx dw shI qrIkw 3√15 hY[ glq qrIkw 3√15 hY[

  7. GxmUl dw phwVw 1 dw GxmUl =1 8 dw GxmUl =2 27 dw GxmUl =3 64 dw GxmUl =4 125 dw GxmUl =5 216 dw GxmUl =6

  8. GxmUl pqw krn dIAW ivDIAw iksy vI ipCly Gx ivc 1+ (n) (n -1) x 3 joVn nwl AglI sMiKAw dw Gx pRwpq huMdw hY, jdoN ik n = 1, 2, 3, 4 _ _ _ hovy[

  9. audwhrx:- 13 = 1 23 = 1+{1+2(2-1) x 3}; {1+(n) (n-1) x 3} jdo n=2 hovy} 33 = 8+{1+3(3-1) x 3} 33 = 8+{1+18} 33 = 27

  10. GxmUl pqw krn dI Aswn ivDI jykr iksy sMiKAw ivcoN qrqIbvwr 1,7,19,37,61,91,127,169,217,271 Gtwaux qy isPr bcy qW sMiKAw pUrn Gx hovygI[ ijMnI vwr Gtwaux qy isPr (0) pRwpq huMdw hY aunW GxmUl hovygw[

  11. audwhrx: kI 216 pUrn Gx hY ? Gtwau ivDI nwl :- 216-1= 215 (1 vwr) 215-7 = 208 (2 vwr) 208-19 = 189 (3 vwr) 189-37 = 152 (4 vwr) 152-61 = 91(5 vwr) 91-91 = 0 (6 vwr)

  12. ieh sMiKAw pUrn Gx hY ikauNik au~qr 0 hY Aqy GxmUl 6 hY[

  13. ABwj guxnKMf rwhI GxmUl pqw krn dI ivDI • sMiKAw dy ABwj guxnKMf bxwey jWdy hn[ • smwn guxnKMf dy iqRgut bxwey jWdy hn[ • jykr pUry iqRgut bxn qW ieh pUrn Gx hY[ • hryk smwn iqRgut ivcoN iek guxnKMf lY ky iehnW dI guxW kIqI jWdI hY[ pRwpq sMiKAw GxmUl hY[

  14. audwhrx: 64 dy ABwj guxnKMf= 2 x 2 x 2 x 2 x 2 x 2 2 dy guxnKMf dy 2 iqRgut bxdy hn ies leI 64 dw GxmUl = 2 x 2 =4 64 dy ABwj guxnKMf= 2 x 2 x 2 x 2 x 2 x 2 2 dy guxnKMf dy 2 iqRgut bxdy hn ies leI 64 dw GxmUl = 2 x 2 =4

  15. tWk qy ijsq sMiKAw dw GxmUl • tWk sMiKAw dw GxmUl tWk sMiKAw huMdI hY[ • irx sMiKAw (-ve) dw GxmUl irx sMiKAw (-ve) huMdI hY[ • ijsq sMiKAw dw GxmUl ijsq sMiKAw huMdI hY[ • Dn sMiKAw (+ve) dw GxmUl Dn sMiKAw (+ve) huMdI hY[

  16. AiBAws

  17. KwlI QwvW Bro [ • vrgmUl ivc ____ dw inSwn vrqdy hW [ • GxmUl ivc ____ dw inSwn vrqWgy [ • 8 dw GxmUl ____ huMdw hY [ • ____ dw GxmUl 3 huMdw hY [ • ____ dw GxmUl 4 huMdw hY [ • 216 dw GxmUl ____ huMdw hY [ • sMiKAw dy ABwj ____ bxwey jWdy hn [ • smwn guxnKMf dy ____ bxwey jWdy hn [ • iqRgut bxn qW ieh pUrn ____ hY [ • iqRgut ivcoN iek guxnKMf lY ky iehnW dI ____ kIqI jWdI hY[

  18. au`qr • vrgmUl ivc √ dw inSwn vrqdy hW [ • GxmUl ivc 3√ dw inSwn vrqWgy [ • 8 dw GxmUl 2 huMdw hY [ • 27 dw GxmUl 3 huMdw hY [ • 64 dw GxmUl 4 huMdw hY [ • 216 dw GxmUl 6 huMdw hY [ • sMiKAw dy ABwj guxnKMf bxwey jWdy hn [ • smwn guxnKMf dy iqRgut bxwey jWdy hn [ • iqRgut bxn qW ieh pUrn Gx hY [ • iqRgut ivcoN iek guxnKMf lY ky iehnW dI guxW kIqI jWdI hY[

  19. Coty pRSnw dy au`qr idE [ • vrgmUl ivc ikhVw inSwn vrqdy hW [ • 8 dw GxmUl kI huMdw hY [ • sMiKAw dy ABwj qo kI bxwey jWdy hn [ • 27 dw GxmUl kI huMdw hY [ • GxmUl ivc ikhVw inSwn vrqWgy [ • smwn guxnKMf qo kI bxwey jWdy hn [ • 64 dw GxmUl kI huMdw hY [ • iqRgut bxn qW kI huMdw hY [ • 216 dw GxmUl kI huMdw hY [ • iqRgut ivcoN iek guxnKMf lY ky kI kIqw jWdw hY[

  20. sroq • Text Book of 8th class • www.Google.com

  21. DnMvwd

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