Hello friend!! Aaj ke iss lesson me hum aapko perfect square number ka square root long division method se nikalana sikhayenge.
Agar aapko square root calculate karne nahi aata hai, square root nikalne me problem hoti hai ya aapko issme doubt rahta hai. To aaj ka ye lesson aapk liye jarur helpful hoga.Aaj hum aapko step-by-step perfect square ka square root long division method se nikalana sikhayenge.
To chaliye aajka lesson start karte hai:
Perfect square ka square root long division method se kaise nikalate hai ?
Hum sabhi jaante hai ki, square root nikalane ke 2 method hai-:
(1). Prime factorization method
(2). Long division method
Prime factorization method se square root nikalana hum pahle se hi aapko sikha chuke hai. Agar aapne abhi tak nahi sikha hai toh nichey humne link diya hai. Aap waha se sikh sakte hai.
Ye bhi padhe-:
❒ square root in few seconds
❒ Square root
❒ Prime factorization method se square root kaise calculate karte hai ?
Aaj hum kewal long division se perfect square ka square root calculate karna sikhayenge.
Sabse pahle hum jaan lete hai ki, jo hum baar-baar perfect square kah rahe hai. Iss perfect square number ka matlab kya hai?
What is a perfect square number?(Perfect square number kya hai?)
Perfect square number ko hindi me "purn varg sankhya" (पूर्ण वर्ग संख्या) kahte hai.
"Perfect square number aisa number hota hai, jisko hum 2 equal integer number ke product (multiplication) ke rup me likh sakte hai."
Example (1). 9 perfect square hai. kyuki 9 ko hum 2 equal integer ke product (multiplication) ke rup me likh sakte hai.
Means, 9 = 3×3
Example (2). 4 perfect square hai kyuki 4 = 2×2
Example (3). 25 perfect square hai kyuki 25 = 5×5
Example (4). 81 perfect square hai kyuki 81 = 9×9
Example (5). 121 perfect square hai kyuki 121 = 11×11
Hume ummid hai ki, ab aap perfect square number ke baare me jaan gaye honge. Ab hum aapko long division method ke baare me batate hai.
Means, 9 = 3×3
Example (2). 4 perfect square hai kyuki 4 = 2×2
Example (3). 25 perfect square hai kyuki 25 = 5×5
Example (4). 81 perfect square hai kyuki 81 = 9×9
Example (5). 121 perfect square hai kyuki 121 = 11×11
Hume ummid hai ki, ab aap perfect square number ke baare me jaan gaye honge. Ab hum aapko long division method ke baare me batate hai.
Long division method kya hai?
Long division method ko hindi me "bhaag vidhi (भाग विधि)" kahate hai. Bhaag vidhi, prime factorization vidhi se easy aur fast hota hai. Jab hume 5 to 6 digit ke number ya iss se bhi jaada digit ke number ka square root nikaalna hota hai toh prime factorization method se time aur steps jaada lagata hai.
Jabki division method se aashani se aur kuch step me square root calculate kiya ja sakta hai.
Agar aap large number (5 se jaada digit) ke number ka square root nikalna chahate hai to hum aapko suggest karenge ki, aap division method ka use kare.
Aap chahe to prime factorization ka bhi use kar sakte hai but division method jaada easy and useful hoga.
Division method ka use kewal large number ke liye hi nahi balki aap iska use small number ke liye bhi kar sakte hai. Small number means, 3 to 4 digit ke number ka bhi square root division method se nikala jaa sakta hai.
Ab hum aapko step-by-step division method ka working rule batane jaa rahe hai. Aap inn steps ko bahot hi dhyaan se padhe aur achhe se samjhe.
Jabki division method se aashani se aur kuch step me square root calculate kiya ja sakta hai.
Agar aap large number (5 se jaada digit) ke number ka square root nikalna chahate hai to hum aapko suggest karenge ki, aap division method ka use kare.
Aap chahe to prime factorization ka bhi use kar sakte hai but division method jaada easy and useful hoga.
Division method ka use kewal large number ke liye hi nahi balki aap iska use small number ke liye bhi kar sakte hai. Small number means, 3 to 4 digit ke number ka bhi square root division method se nikala jaa sakta hai.
Ab hum aapko step-by-step division method ka working rule batane jaa rahe hai. Aap inn steps ko bahot hi dhyaan se padhe aur achhe se samjhe.
Square root Long division method ka Working Steps :
Step-1. Sabse pahle jis number ka square root nikalana hai uss number ka unit's digit (इकाई) se pair (joda) banaye aur sabhi pair ke uppar "baar" (￣) lagaye.
Jaise-: (1). √1024 = ??
1024 me unit's digit 4 se pair banana start karenge.
10 , 24 = 2 pairs
(2).√125316 = ??
12 , 53 , 16 = 3 pairs
Agar koi number ka pair nahi banta hai to ussko bhi ek pair hi maanenge. Jaise aap nichey diye examples dekhiye.
(3). √23716
23716 me 16 aur 37 ka pair banta hai lekin 2 ka pair nahi bana to isko bhi hum ek pair hi maanenge.
2 , 37, 16 = 3 pairs
(4). √1028196
1 , 02 , 81 , 96 = 4 pairs
Chaliye hum isske aage ke step ko ek question ko solve karte huye sikhate hai:
Question: √225 = ??
Solution-: Hume 225 ka square root division method se nikalana hai toh isske liye hum nichey diye steps ko follow karenge.
Step-1. Sabse pahle unit's digit 5 se pair banaye.
2 , 25 = 2 pairs
Jaise-: (1). √1024 = ??
1024 me unit's digit 4 se pair banana start karenge.
10 , 24 = 2 pairs
(2).√125316 = ??
12 , 53 , 16 = 3 pairs
Agar koi number ka pair nahi banta hai to ussko bhi ek pair hi maanenge. Jaise aap nichey diye examples dekhiye.
(3). √23716
23716 me 16 aur 37 ka pair banta hai lekin 2 ka pair nahi bana to isko bhi hum ek pair hi maanenge.
2 , 37, 16 = 3 pairs
(4). √1028196
1 , 02 , 81 , 96 = 4 pairs
Chaliye hum isske aage ke step ko ek question ko solve karte huye sikhate hai:
Question: √225 = ??
Solution-: Hume 225 ka square root division method se nikalana hai toh isske liye hum nichey diye steps ko follow karenge.
Step-1. Sabse pahle unit's digit 5 se pair banaye.
2 , 25 = 2 pairs
Step-2. First pair (left side se) 2 ko dividend (bhaajak) maankar divide karna start karenge.
Isske liye aisa largest number maalum kariye jiska square first pair number (left side se) 2 ke equal ho ya to less (kam) ho.
Means, 1²<2<2² , isliye 1 ko choose karenge.
Iss number 1 ko divisor (bhaajya) aur isske square 1² = 1 ko dividend (2) ke nichey likh kar remainder (sheshphal) 2-1 = 1 maalum karenge. (Nichey diya image dekhiye)
Isske liye aisa largest number maalum kariye jiska square first pair number (left side se) 2 ke equal ho ya to less (kam) ho.
Means, 1²<2<2² , isliye 1 ko choose karenge.
Iss number 1 ko divisor (bhaajya) aur isske square 1² = 1 ko dividend (2) ke nichey likh kar remainder (sheshphal) 2-1 = 1 maalum karenge. (Nichey diya image dekhiye)
Step-3. Remainder 1 ke right side me next pair (25) ko likhe. Jiss se hume next dividend (125) milega.
Step-4. Ab divisor (iss question me 1) ko 2 guna karke (1×2 = 2) likhe. Ye new divisor hai but complete nahi hai ye kewal ek bhaag hai aur isske right side me space (khaali jagah) rahne dijiye.
Step-5. Iss space (khaali jagah) me hume ek number (iss question ke liye 5) likhna hai. Ye number (5) next quotient bhi hoga.
Number (5) ko space me rakhte hi new divisor (25) complete ho jaayega.
Ye yaad rakhe ki space me aisa number (5) likhana hai ki, new divisor (25) aur next quotient (5) se multiply (25×5) karne par multiplication (25×5=125), Step-3. ke dividend (125) ke equal ho ya less ho.
Iss question me equal hai. (Nichey diya image dekhiye)
Hum dekh sakte hai ki, humne sabhi pair ko lekar division complete kar liya hai.
Isliye, √225 = 15 Ans.
Step-6. Aapko Step-2. se Step-5. ko tab tak karna hai jab tak sabhi pair complete naa ho jaaye.
Pair complete hone par quotient hi diye huye number ka square root hoga.
Hume ummid hai ki, aapko division method ke sabhi steps achhe se samjh aaye honge. Agar aapko koi doubt hai to abhi comment karke puchhiye.
Square root long division method ke Question and Solution:
Que.-1: Long division method se 841 ka square root gyaat kijiye.
Solution: √841 ke liye sabhi steps diye gaye hai-:
∴ √841 = 29 Answer
Que.-2: Long division method se 1764 ka square root gyaat kijiye.
Solution: √1764 ke liye sabhi steps diye gaye hai-:
∴ √1764 = 42 Answer
Que.-3: 5476 ka square root division method se nikaliye.
Solution: √5476 ke liye sabhi steps diye gaye hai-:
∴ √5476 = 74 Answer
Que.-4: √15,376 ka bhaag vidhi se vargmul gyaat kijiye.
Solution: √15,376 ke liye sabhi steps diye gaye hai-:
∴ √15,376 = 124 Answer
Que.-5: √29,929 ka bhaag vidhi se vargmul gyaat kijiye ??
Solution: √29,929 ke liye sabhi steps diye gaye hai-:
∴ √29,929 = 173 Answer
Ye bhi sikhiye-:Number (5) ko space me rakhte hi new divisor (25) complete ho jaayega.
Ye yaad rakhe ki space me aisa number (5) likhana hai ki, new divisor (25) aur next quotient (5) se multiply (25×5) karne par multiplication (25×5=125), Step-3. ke dividend (125) ke equal ho ya less ho.
Iss question me equal hai. (Nichey diya image dekhiye)
Hum dekh sakte hai ki, humne sabhi pair ko lekar division complete kar liya hai.
Isliye, √225 = 15 Ans.
Step-6. Aapko Step-2. se Step-5. ko tab tak karna hai jab tak sabhi pair complete naa ho jaaye.
Pair complete hone par quotient hi diye huye number ka square root hoga.
Hume ummid hai ki, aapko division method ke sabhi steps achhe se samjh aaye honge. Agar aapko koi doubt hai to abhi comment karke puchhiye.
Square root long division method ke Question and Solution:
Que.-1: Long division method se 841 ka square root gyaat kijiye.
Solution: √841 ke liye sabhi steps diye gaye hai-:
∴ √841 = 29 Answer
Que.-2: Long division method se 1764 ka square root gyaat kijiye.
Solution: √1764 ke liye sabhi steps diye gaye hai-:
∴ √1764 = 42 Answer
Que.-3: 5476 ka square root division method se nikaliye.
Solution: √5476 ke liye sabhi steps diye gaye hai-:
∴ √5476 = 74 Answer
Que.-4: √15,376 ka bhaag vidhi se vargmul gyaat kijiye.
Solution: √15,376 ke liye sabhi steps diye gaye hai-:
∴ √15,376 = 124 Answer
Que.-5: √29,929 ka bhaag vidhi se vargmul gyaat kijiye ??
Solution: √29,929 ke liye sabhi steps diye gaye hai-:
∴ √29,929 = 173 Answer
❒ Speed , distance and time part-1
❒ BODMAS rule ka use kark 10 question solve karna sikhiye.
❒ BODMAS rule part-1
Toh friend hume ummid hai ki, ab aap perfect square ka square root long division method se nikalana sikh gaye honge.
Agar aapko abhi bhi iss lesson me koi doubt hai, problem hai ya aap koi question puchhna chahte hai to abhi comment karke puchh sakte hai.
Aap apna question humare Facebook page par massage karke bhi bhej sakte hai. Humara Facebook page nichey diya gaya hai.
Hum issi tarah math ke ek-ek topic ko likhkar aapki mathematics strong banane ki koshish kar rahe hai. Aap hume bataye ki, Next lesson me aap kon-sa math ka topic sikhna chahate hai? Abhi comment ya massage karke bataye.
Hum uss topic ke baare me full details me aapko sikhayenge.
Agar aapko aaj ka lesson helpful laga ho to please ek share karke humari help kijiye.
Thank you sir, you taught me this formula of maths in a very easy way.
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