गुरुवार, जून 11, 2015

square root in few seconds

Hello friends !  maths tricks in Hindi  me aap ka swagat hai. Friends aapne mera pichhala post Fast multiply by 11 in Hindi  ko jarur read kiya hoga ,jisme maine 11 k saath kisi number ka multiply karne ka fast tarika bataya tha.
Friends Aaj mai aapko batauga ki aap " kisi numbers ka square root (vargamool) tricks ya shortcuts se kaise kar sakte hai ? "
square root in few seconds

Square root ( vargamool ) kya hota hai? 

Square root ko hindi me " वर्गमूल "(vargamool )" kahate hai. Kisi number ka square root nikalane ka matalab hai, ki ye pata karna ki wo kis number ka square hai.
For ex-: 25 , 5 ka square hai, Isliye 25 ka square root 5 hai. 
√25=5 


Also read -:
General method se hum Square root Two tarike se nikalte hai.
1. Division method
2. Multiplication method
Ye dono general methods hai.

Square root tricks se kyu Kare? 

Square root ko tricks se kyu Kare iss baare me mujhe nhi lagata aapko Jada kuch batane ki jarurat hai, kyuki hum jaante hai ki square root genral method se nikalana kitana kathin ( tough) hota hai. General method se time bhi Jada lagata hai. Isliye hum square root tricks se aashani aor jaldi se laga sakate hai.
 Aap meri tricks ka use kark aasani oar jaldi se kisi bhi number ka square root ( vargamool) nikal sakate hai . Chaliye start karte hai. To aaj hum shikhege ki -:

Kisi number ka square root ( vargamool ) trick ya shortcuts se kaise solve karte hai? 

Friends iss trick ka use hum only unn number ka square root nikalne me kar sakte hai jo kewal 4 digit tak k number ho.
For example-:  169, 2304, 3136 etc.
But hum 4 digit se adhik number ka square root iss tricks se nhi kar sakte.

Also read -:
• what are prime numbers and composite numbers ?




To start karte hai -:
Iss square root shortcut ka use karne k liye apko 1 se 9 tak k number ka square yaad rakhna hai.Jo maine niche "square table" image me diya hai -:
Square roots in few seconds
Square table

Friends hum chhahe 3 digit k number ka square root nikale ya 4 digit k number ka square root humesha square root ka answer 2 digit me aayega.
Means  suppose karte hai ki ek 4 digit ka number hai = XXXX
To isska square root = √XXXX
                                      =  xy
Issi type se 3 digit ka number = xxx
Iska square root = √xxx
                               = xy
Jaha par ,  x = tens place ka number.
         y = ones place ka number.

Ab square root ko trick se nikalna shikhate hai-:
Friends hum square root ko following step me nikalenge-:
(a) tens place (x) ki value shortcut se 
 (b) ones place (y) ki value shortcut se 



Aap niche diye rules ko follow kare-:
Chaliye ek example lekar aaj ka shortcut start karte hai-:
Example-1. Square root of 529
 Trick-:  Suppose karte hai ki
               √529 = xy
Jaha par , x = tens place ka number
                  y = ones place ka number
Jaisa ki mai bata chuka hu ki  Square root hum two important step me nikalenge-:
Step-(a) 529 k square root k tens place
               ka number "x"
Step-(b) 529 k square root k ones place
               ka number "y"
(a)  529 k square root k tens place (x) -:
 529 k square root k tens place ka number "x" ki value -
Step-1. 529 ka left side se first no. = 5
Step-2. Square table se ,
             2 ka square = 4
And 4<5 hai.
Isliye 2 , 529 k square root k tens place (x) ka number hoga.
( note -: 3 ka square = 9 > 5 isliye hum 3 ko nhi le sakte.)
Isliye "x" = 2
Means √529 = 2y
Ab hume "y" ki value find karni hai.

(b) 529 k square root k ones place(y) 
 529 k square root k ones place(y) ki value-:
Step-1. 529 ka last digit = 9
Step-2 square table se ,
            3 ka square =  9 
            7 ka square = 4  9 
Hum dekh sakte hai ki 3 and 7 k square k ones place par "9" hai .
Isliye 529 k square k ones place(y)
= 3 ya 7 hoga. ( only one)

 3 ya 7 me kon hoga -:
 3 ya 7 me ones place (y) ki value kon sa number hoga iskliye follow step-:
Step-3. Formula -:
            (x+1)×x
 Iss formula me "x" ki value rakhe aor solve kare-:
"x" = 2
=(2+1)×2
= 6
But 6 >5 hai . Isliye hum 3 and 7 me se smaller (3<7) value 3 lenge.
To "y" = 3
Means √529 = 23 Ans.
 Niche diya video jarur dekhe aapko jarur help milegi.


Example-2.     √2304
 Trick-: suppose karte hai ki -:
√2304 =  x y 
x= tens place ka number.
y= ones place ka number.
Tens place (x) ka number nikalne ka shortcut -:
Tens place (x) ka number shortcut se hum 2 step me nikalana shikhenge.
Step-1. 2304 ka left side se 2 digit
               = 23
Step-2. Square table se -:
                4 ka square = 16<23
But 5 ka square = 25>23.
Isliye tens place(x) = 4
Means "x" = 4
√2304 = 4 y 
 Ab hum "y" ki value ko find karenge.
Ones place(y) digit ka number shortcut se -:
 Ones place(y) ki value hum 3 step me nikalenge-:
Step-1. 2304 ka last digit = 4
Step-2. Square table se -:
             2 ka square =  4 
             8 ka square = 6 4 
Means 2 and 8 k square k ones place par 4 hai . Isliye 2304 k square root k ones place par ya to 2 hoga ya 8 hoga.

 2 ya 8 me se kon hoga -:
 2 ya 8 me se kon ones place(y) ka value hoga.iskliye follow step.
Step-3. Niche diye formula me "x" ki value rakhe oar solve kare-:
(x+1)×x
=(4+1)×4
=20
But 20<23 hai isliye hum 2 and 8 me se greater number 8 ko lenge.
Means ones place(y) = 8
√2304 = xy
           = 48 Ans.

Example-3. Square root of 3136.
Trick-: Hum jaante hai ki 3136 ka square root two digit ka hoga.
"3136 ka square root = √ 3136
                                       = xy
x= tens place number.
y= ones place number.

Isliye first hum "tens place" k number ko tricks se nikalenge. Uss k baad " ones place" ko.

Tens place (x) nikalne k liye shortcut -:

3136 k square root k tens place hum 2 step me shikhege.
Step-1. 3136 ka left side se two digit                    choose kare.
Left side se two digit = 31
Step-2. Ab upper diye square table se
            uss number ko choose kare jiska square 31 k equal ho ya small ho.
Table me dekhne k baad hume pata chalta hai ki -
5 ka square = 25<31 hai.
Isliye 3136 k square root ka tens place ka number "5" hoga.
Means " 3136 k square root k tens place(x) = 5 "

Ones place (y) nikalne k liye shortcut -:
 Ones place(y) nikalne k liye 3 step ko follow kare.
Step-1. 3136 ka last digit=6
Step-2. Ab square table me uss number ko choose kare jisk square k "ones place" par "6" ho.
4 ka square= 1 6 
6 ka square= 3 6 

Ab 4 ya 6 me se koi ek number 3136 k square root k ones place ka number hoga.
 4 ya 6 me se ko ones place ka number hoga ?
 Step ko follow kare-:
Step-3. 3136 k square root ka tens place(x) = 5
Step-4. "x" ki value niche diye formula me rakhe aor solve kare.
Formula-:
                   (x+1)×x
 = (5+1)×5
= 30
Hum dekh sakte hai ki 30<31 .
Isliye 4 and 6 me se jo number greater(4<6) 6 ones place ka number hai.
Means ones place(y)=6
Isliye 3136 k square root = xy
                                              = 56  Ans.
Example-4. √784 = ?
Trick-:  suppose karte hai ki
              √784 = xy
 "x" ki value k liye -:
 Step-1. 784 ka left side se first no. = 7
Step-2.  Square table se ,
              2 ka square = 4
And 4 < 7
Isliye "x" = 2
 "y" ki value k liye -:  
 Step-1. 784 ka last digit = 4
Step-2. Square table se,
             2 ka square =  4  
             8 ka square = 6  4 
 Means "y" = 2 or 8
 2 or 8 me se kon hoga -:
 Step-3. Formula -:
(x+1)×x
= (2+1)×2
= 6
And 6 < 7  isliye 2 and 8 me se smaller no.(2<8) 2 , "y" ki value hoga.
"y" = 2
 Means √784 = xy
                        = 28 Ans.

Example-5. √1681 = ?
 Trick-: suppose √1681 = xy
 "x" ki value-:
 Step-1. 1681 ka left side se two digit
               = 16
Step-2. Square table se ,
             4 ka square = 16 = 16
 Isliye "x" = 4
 Ab hume "y" ki value find karna hai.

"y" ki value-:
Step-1. 1681 ka last digit = 1
Step-2. Square table se,
             Hum dekhte hai ki 1 k square and 9 k square k ones place par "1" hai.
             1 ka square =  1 
             9 ka square = 8 1 
Isliye "y" = 1 or 8

1 ya 8 me se kon -:
Step-3. "x" = 4 ki value formula -:
            (x+1)×x me rakhne aor solve kare.
(4+1)×4
=20
20 >16 isliye hum 8>1 me se smaller value "1" lenge.
Means "y" = 1
√1681 = xy
            = 41 Ans.
           
   Special number square root shortcut


Last digit 5 wale numbers ka square root shortcut -:

 Friends jis number ka Last digit 5 wale numbers ka square karna hum shikh chuk hai. Aaj hum last digit 5 wale number ka square root tricks se karna jaanege.
 For example-: 2025,1225, 625 , etc.
To inn types k numbers ka square root aap dekhte hi answer batata sakate hai.
Matlab " no use pen and no use paper".
Square root in just your mind.
Aap soch rahe honge kaise ? Chaliye mai batata hu kaise.
Iss type k number ka square root 2 easy step me nikal sakte hai.
Step-1. Diye gaye number ka tens place
             Digit number (x) nikalenge.
Step-2. Diye number ka ones place digit
              number "y" = 5 hoga.

Example-6.  √2025 = ?
Trick-: Suppose √2025 = xy
                                         = x5
Ab hume kewal "x" ki value find karna hai.
 Tens place (x) ka number -:
 Step-1. 2025 ka left side se 2 digit= 20
Step-2. Square table se ,
             4 ka square = 16
Ab 16<20 hai isliye "x" = 4
[Note-: hum "x"=5 nhi choose kar sakte because 5 ka square =25>16]
Isliye √2025 =x5
                      = 45 Ans.

Example-7. √625 =?
Trick-: √625 = xy
But "y" = 5
√625 = x5
 Tens place (x) ki value -:
 Step-1. 625 ka left side se first digit=6
Step-2. Square table se,
             2 ka square = 4<6
Isliye "x"= 2
√625 = x5
         = 25 Ans.

Ex-8. √5625 =?
 √5625 = x5
 "x" ki value k liye -:
 Step-1. 5625 ka left side se 2 digit = 56
Step-2.  Square table se ,
              7 ka square = 49<56
Isliye "x"= 7
√5625 = x5
            = 75 Ans.

Ex-9. √225 =?
 Trick-: √225 = x5
x ki value k liye -:
 Step-1. 225 k left side se first digit = 2
Step -2. Square table se,
               1 ka square = 1
1<2
Isliye "x" = 1
√225 = x5
         = 15 Ans.
Square root in few seconds bus itana hi. Aapko aaj ka ye square root shortcut trick kaisa laga ? Please comment kark hume jarur bataye.
Aap hume Facebook page and Twitter par follow kark new post ki jaankari jaldi pa sakte hai.
Aor share karna mat bhuliyega.
Thanks for reading!☺☺☺

30 टिप्‍पणियां:

  1. Dayanand Deshmukh ji abhi ye method pura nhi huaa hai.mai Kuch aor example dunga tb apko method sahi lagega

    जवाब देंहटाएं
  2. उत्तर
    1. manish sharma ji example-3 dekhe.aapko aapka answer mil jayega.
      Koi oar problem ho to jarur puchhiyega.

      हटाएं
    2. LAST DIGIT DEKHENGE
      JO KI 6 HEIN.
      4 OR 6 KE SQ. KE LAST ME AATA H 6.
      EX. 4=16
      6=36

      MEANS LAST DIGIT 4 YA 6 HOGA


      AB STARTIND KE 2 DIGIT LE LO JO KI 31 HEIN.


      AB 31 TO KISI KA SQ. HE NHI.. TO 31 SE CHOTA KISI KA SQ. DEKHENGE...



      5 KA SQ. HOTA H 30
      OR
      6 KA SQ HOTA H 36



      IS LIYE 5 KO LENGE


      AB DONO DIGIT PTA H HMKO..



      1ST = 54

      2ND = 56





      AB 55 KA SQ. DEKH LO KI KYA H...(15.25.35.45.55.65.75.....KA SQ. NIKALNA KAFI ESSY H ISKI TRICK BHOOT HI SIMPLE H. APKO BHI AATI HI HOGI)


      55 KA SQ. HEIN 3025

      3025<3136(3025 CHOTA H 3136 SE )
      IS LIYE BDI SANKLHYA LENGE....JO KI 56 HEIN.


      THATS IT !!

      हटाएं
  3. Achcha sir hme pta kaise chalega ki kon sa √number is trick ke liye he jaise...
    √2025=25 to is trick me kam kr rh he but agr question me
    √4375=? de diya tb kya krenge ye to is trick se nhi hoga.
    to aakhir me pta kaise kre ki kon √number is trick ke liye he or kon nhi.

    जवाब देंहटाएं
    उत्तर
    1. Rahul kumar sharma ji aapne bahot hi accha question pucha hai.
      Ye trick kewal perfect square root wale number par use kar sakte hai.
      For example aapne jo no. 4375 liya hai iska square root 66.14(approx) hai. Jo ki perfect square root nhi hai.
      I hope aapko aapk question ka answer mil gaya ho.
      Koi aor question ho to jarur puchhe.

      हटाएं
  4. muje is 172.3969 question na square root nikalna ho to kaise nikal sakta hoon ???

    जवाब देंहटाएं
  5. 676 ka square root kese nikalenge??

    xy=2y

    y ka maan kese nikalenge
    b/w 4 & 6

    Reply fast please

    जवाब देंहटाएं
    उत्तर
    1. 676 ka square root aap uppar post me diye method se aashani se kar sakte hai.

      हटाएं
    2. sir 676 k square root nikalne p apka method fail ho rha h as y nikalne k liye jb 2*3=6 krte h to wo 676 k 6 k equal aa rha h.. jisk karn ye kaise decide kre k 4 le ya 6...

      हटाएं
    3. Aapne sahi kaha . 676 ke liye ye trick work nahi kar paa raha hai.
      Hum jald hi isska koi solution nikalenge. Tab tak aapko wait karna padega. Thanks for comment !!

      हटाएं
  6. Mem please 4 se adhik digit ke square roote nikalne ki trick bataye

    जवाब देंहटाएं
    उत्तर
    1. Ji jarur, hum jald hi 4 se adhik digit ka square root nikalne ki trick batayenge. Keep visiting !

      हटाएं
  7. उत्तर
    1. √585000 ka square root long division method se solve hoga. Long division method me humne perfect square waale number ka square root nikalana bata chuke hai. Lekin humne non perfect square waale number ka square root nikalana abhi nahi bataya hai. Hum jald hi issko batayenge.

      हटाएं