#🙏ఓం నమః శివాయ🙏ૐ #శివ పంచాక్షరి స్త్రోత్రం🙏🌷శివోహం🙏 🙏🔥!!.శివ పంచాక్షరీ స్తోత్రము.!!🔥🙏🕉️🌿🕉️🌿🕉️🌿🕉️🌿🕉️🌿🕉️🌿🕉️🌿🕉️
నాగేంద్రహారాయ త్రిలోచనాయ భస్మాంగరాగాయ మహేశ్వరాయ
నిత్యాయ శుద్ధాయ దిగంబరాయ తస్మై నకారాయ నమశ్శివాయ ...1
మందాకినీ సలిల చందన చర్చితాయ నందీశ్వర ప్రమథ నాథ మహేశ్వరాయ
మందార పుష్ప బహు పుష్ప సుపూజితాయ తస్మై మకారాయ నమశ్శివాయ ...2
శివాయ గౌరీ వదనారవింద-సూర్యాయ దక్షాధ్వర నాశకాయ
శ్రీ నీల కంఠాయ వృషధ్వజాయ తస్మై శికారాయ నమశ్శివాయ ...3
వశిష్ఠ కుంభోద్భవ గౌతమాది మునీంద్ర దేవార్చిత శేఖరాయ
చంద్రార్క వైశ్వానర-లోచనాయ తస్మై వకారాయ నమశ్శివాయ ...4
యజ్ఞ స్వరూపాయ జటాధరాయ పినాక హస్తాయ సనాతనాయ
దివ్యాయ దేవాయ దిగంబరాయ తస్మై యకారాయ నమశ్శివాయ ...5
ఫలశృతి
పంచాక్షర-మిదం పుణ్యం యః పఠేత్ శివ సన్నిధౌ
శివలోక-మవాప్నోతి శివేన సహ మోదతే.!!
🌷🌼🌷🌼🌷🌼🌷🌼🌷🌼🌷🌼🌷🌼🌷
![🏆పోటీ పరీక్షల స్పెషల్ - EAPCET (APITG (CSX-Sx)(2+2Simدx) NDA BITSAT KET JEE Mag] Cx +Sim) Si2x +C ((G31-Sim)2 (1+Simn2x)dz C22 + C 2) Cx+Simz) TO२ ७ + c 3) (Cogat-Suna) (($2+Sun 7 Ct 21 +C 2SmzGxd) 2 Cox+sim ) (Cx - Smx ) (0Sx(+Sunx) dz 2 ((81+Smnx) ( (CSit-Simz) (CoBx+Simx) dsc 2 २( (@९ 2 X-Simz) dx =2 ( (82x dx 2 ( Smzz) +c MATH Solutions By PHANI Sin2+C / B @MATH Solutions @Phaneendra Va PHAN EAPCET (APITG (CSX-Sx)(2+2Simدx) NDA BITSAT KET JEE Mag] Cx +Sim) Si2x +C ((G31-Sim)2 (1+Simn2x)dz C22 + C 2) Cx+Simz) TO२ ७ + c 3) (Cogat-Suna) (($2+Sun 7 Ct 21 +C 2SmzGxd) 2 Cox+sim ) (Cx - Smx ) (0Sx(+Sunx) dz 2 ((81+Smnx) ( (CSit-Simz) (CoBx+Simx) dsc 2 २( (@९ 2 X-Simz) dx =2 ( (82x dx 2 ( Smzz) +c MATH Solutions By PHANI Sin2+C / B @MATH Solutions @Phaneendra Va PHAN - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_49408_2428fdc3_1768875048154_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=154_sc.jpg "🏆పోటీ పరీక్షల స్పెషల్ - EAPCET (APITG (CSX-Sx)(2+2Simدx) NDA BITSAT KET JEE Mag] Cx +Sim) Si2x +C ((G31-Sim)2 (1+Simn2x)dz C22 + C 2) Cx+Simz) TO२ ७ + c 3) (Cogat-Suna) (($2+Sun 7 Ct 21 +C 2SmzGxd) 2 Cox+sim ) (Cx - Smx ) (0Sx(+Sunx) dz 2 ((81+Smnx) ( (CSit-Simz) (CoBx+Simx) dsc 2 २( (@९ 2 X-Simz) dx =2 ( (82x dx 2 ( Smzz) +c MATH Solutions By PHANI Sin2+C / B @MATH Solutions @Phaneendra Va PHAN EAPCET (APITG (CSX-Sx)(2+2Simدx) NDA BITSAT KET JEE Mag] Cx +Sim) Si2x +C ((G31-Sim)2 (1+Simn2x)dz C22 + C 2) Cx+Simz) TO२ ७ + c 3) (Cogat-Suna) (($2+Sun 7 Ct 21 +C 2SmzGxd) 2 Cox+sim ) (Cx - Smx ) (0Sx(+Sunx) dz 2 ((81+Smnx) ( (CSit-Simz) (CoBx+Simx) dsc 2 २( (@९ 2 X-Simz) dx =2 ( (82x dx 2 ( Smzz) +c MATH Solutions By PHANI Sin2+C / B @MATH Solutions @Phaneendra Va PHAN - ShareChat")
![👩💻టెట్/DSC ప్రత్యేకం - Ch-6: Squares ond Squqre Roots Part 3 MATH/ Square Roots (Inverse operation of Squaring) Solutions 5. By PHANI Definition: Finding the square root_is the inverse] operation of squaring The symbol for 1 squgre root is Examples: Since 42 16, therefore 16 4 Since 42 = 16, therefore V81 4 Since 92 81, therefore 181 9 = Finding Square Root by Prime Factorization 6. 1. Find_prime factors: Method: Make pairs of equal factors 2. Make pairs of equal factors 2. Take one factor from each and 3. pair multiply: Example: Find the square root of ३२४. 324 324 2x2x3x3x3x3 2 = 324 162 2x2x3x3x3x3 2 5 162 2 1(2*2) * (3*3) * (3*3) 1324 81 3 3 27 3 1324 2*3*3 3 9 = 3 3 _324 18 Note: Useful for perfect squares Ch-6: Squares ond Squqre Roots Part 3 MATH/ Square Roots (Inverse operation of Squaring) Solutions 5. By PHANI Definition: Finding the square root_is the inverse] operation of squaring The symbol for 1 squgre root is Examples: Since 42 16, therefore 16 4 Since 42 = 16, therefore V81 4 Since 92 81, therefore 181 9 = Finding Square Root by Prime Factorization 6. 1. Find_prime factors: Method: Make pairs of equal factors 2. Make pairs of equal factors 2. Take one factor from each and 3. pair multiply: Example: Find the square root of ३२४. 324 324 2x2x3x3x3x3 2 = 324 162 2x2x3x3x3x3 2 5 162 2 1(2*2) * (3*3) * (3*3) 1324 81 3 3 27 3 1324 2*3*3 3 9 = 3 3 _324 18 Note: Useful for perfect squares - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_230535_11412d_1768802228948_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=948_sc.jpg "👩💻టెట్/DSC ప్రత్యేకం - Ch-6: Squares ond Squqre Roots Part 3 MATH/ Square Roots (Inverse operation of Squaring) Solutions 5. By PHANI Definition: Finding the square root_is the inverse] operation of squaring The symbol for 1 squgre root is Examples: Since 42 16, therefore 16 4 Since 42 = 16, therefore V81 4 Since 92 81, therefore 181 9 = Finding Square Root by Prime Factorization 6. 1. Find_prime factors: Method: Make pairs of equal factors 2. Make pairs of equal factors 2. Take one factor from each and 3. pair multiply: Example: Find the square root of ३२४. 324 324 2x2x3x3x3x3 2 = 324 162 2x2x3x3x3x3 2 5 162 2 1(2*2) * (3*3) * (3*3) 1324 81 3 3 27 3 1324 2*3*3 3 9 = 3 3 _324 18 Note: Useful for perfect squares Ch-6: Squares ond Squqre Roots Part 3 MATH/ Square Roots (Inverse operation of Squaring) Solutions 5. By PHANI Definition: Finding the square root_is the inverse] operation of squaring The symbol for 1 squgre root is Examples: Since 42 16, therefore 16 4 Since 42 = 16, therefore V81 4 Since 92 81, therefore 181 9 = Finding Square Root by Prime Factorization 6. 1. Find_prime factors: Method: Make pairs of equal factors 2. Make pairs of equal factors 2. Take one factor from each and 3. pair multiply: Example: Find the square root of ३२४. 324 324 2x2x3x3x3x3 2 = 324 162 2x2x3x3x3x3 2 5 162 2 1(2*2) * (3*3) * (3*3) 1324 81 3 3 27 3 1324 2*3*3 3 9 = 3 3 _324 18 Note: Useful for perfect squares - ShareChat")
![👩💻టెట్/DSC ప్రత్యేకం - Squares and Square Roots Ch-6: Part 2 MATH / Interesting_Patterns Solutions 3. By PHANI 0) Sum of first 'n' odd natural numbers is n2 Examples: 1=1=.12 1+324222 1 + 3 + 5 = 9 = 32 1+3+ 5+ 7=16 = 42 b) Numbers between consecutive_square numbers n2 qnd (n+1)2' are 2n' non square numbers between There n2_and (n+1)2, Exqmple: Between 32 and 42= 16 9 = n=3. Non-squqre numbers 2n = 2*3 = 6. Here They are 10, 11, 12, 13, 14, 15. Pythagorean Triplets 4. Definition: set of three numbers (a, b, c) that A such 02 + b2 = C2 Generql Form: For qny integer m > 1, the triplet is (2m, m2-1, m2+1) Example: Find triplet whose one member is 12. a Let 2m = 12 m = 6. First member 2m = 12. m2 - ] = 62 - ] = 36 - ] = 35. Second member member = m2 + ] = 62 + ] = 36 + ] = 37. Third Triplet is (12,35, 37) Check: 122 + 352 = 144 + 1225 = 1369 = 372. (Correctl) Squares and Square Roots Ch-6: Part 2 MATH / Interesting_Patterns Solutions 3. By PHANI 0) Sum of first 'n' odd natural numbers is n2 Examples: 1=1=.12 1+324222 1 + 3 + 5 = 9 = 32 1+3+ 5+ 7=16 = 42 b) Numbers between consecutive_square numbers n2 qnd (n+1)2' are 2n' non square numbers between There n2_and (n+1)2, Exqmple: Between 32 and 42= 16 9 = n=3. Non-squqre numbers 2n = 2*3 = 6. Here They are 10, 11, 12, 13, 14, 15. Pythagorean Triplets 4. Definition: set of three numbers (a, b, c) that A such 02 + b2 = C2 Generql Form: For qny integer m > 1, the triplet is (2m, m2-1, m2+1) Example: Find triplet whose one member is 12. a Let 2m = 12 m = 6. First member 2m = 12. m2 - ] = 62 - ] = 36 - ] = 35. Second member member = m2 + ] = 62 + ] = 36 + ] = 37. Third Triplet is (12,35, 37) Check: 122 + 352 = 144 + 1225 = 1369 = 372. (Correctl) - ShareChat](https://cdn4.sharechat.com/bd5223f_s1w/compressed_gm_40_img_200099_31576703_1768802198814_sc.jpg?tenant=sc&referrer=user-profile-service%2FrequestType50&f=814_sc.jpg "👩💻టెట్/DSC ప్రత్యేకం - Squares and Square Roots Ch-6: Part 2 MATH / Interesting_Patterns Solutions 3. By PHANI 0) Sum of first 'n' odd natural numbers is n2 Examples: 1=1=.12 1+324222 1 + 3 + 5 = 9 = 32 1+3+ 5+ 7=16 = 42 b) Numbers between consecutive_square numbers n2 qnd (n+1)2' are 2n' non square numbers between There n2_and (n+1)2, Exqmple: Between 32 and 42= 16 9 = n=3. Non-squqre numbers 2n = 2*3 = 6. Here They are 10, 11, 12, 13, 14, 15. Pythagorean Triplets 4. Definition: set of three numbers (a, b, c) that A such 02 + b2 = C2 Generql Form: For qny integer m > 1, the triplet is (2m, m2-1, m2+1) Example: Find triplet whose one member is 12. a Let 2m = 12 m = 6. First member 2m = 12. m2 - ] = 62 - ] = 36 - ] = 35. Second member member = m2 + ] = 62 + ] = 36 + ] = 37. Third Triplet is (12,35, 37) Check: 122 + 352 = 144 + 1225 = 1369 = 372. (Correctl) Squares and Square Roots Ch-6: Part 2 MATH / Interesting_Patterns Solutions 3. By PHANI 0) Sum of first 'n' odd natural numbers is n2 Examples: 1=1=.12 1+324222 1 + 3 + 5 = 9 = 32 1+3+ 5+ 7=16 = 42 b) Numbers between consecutive_square numbers n2 qnd (n+1)2' are 2n' non square numbers between There n2_and (n+1)2, Exqmple: Between 32 and 42= 16 9 = n=3. Non-squqre numbers 2n = 2*3 = 6. Here They are 10, 11, 12, 13, 14, 15. Pythagorean Triplets 4. Definition: set of three numbers (a, b, c) that A such 02 + b2 = C2 Generql Form: For qny integer m > 1, the triplet is (2m, m2-1, m2+1) Example: Find triplet whose one member is 12. a Let 2m = 12 m = 6. First member 2m = 12. m2 - ] = 62 - ] = 36 - ] = 35. Second member member = m2 + ] = 62 + ] = 36 + ] = 37. Third Triplet is (12,35, 37) Check: 122 + 352 = 144 + 1225 = 1369 = 372. (Correctl) - ShareChat")
