Question

how to take square root of 22801 number??

Answer 1

just find a no. near to that of which you know sq root and then use differentiation..

Answer 2

STEP1.........Pair your numbers from the right

Answer 3

STEP2......Take the first number from the left (here it is 2) and think of a number whose square is less than or equal to the number
Here it is 1

Answer 4

1*1 =1........I will write 1 on the left and 1 on the top .......>>>Also subtract 1 frm 2 (1 is the remainder)

Answer 5

Simultaneously add 1+1 =2

Answer 6

STEP 3.....Now bring down the next pair.........u get 128......>>>>>Think of a number such that 2? *? <=128...........here '?' is a single digit number

Answer 7

I found that 25*5 =125<128

Answer 8

Thanks a lot @ atlas

Answer 9

Now again I write 5 on the top and add 25+5=30

Answer 10

continue the process till u get 0

Answer 11

nice!
a big round of applause for @atlas
*claps*

Answer 12

haha.........thanks :)

Answer 13

I really didnt get that method

Answer 14

Can you please explain it

Answer 15

yeah sure

Answer 16

similarly find the square root of 469225

Answer 17

you got it till what point

Answer 18

till pairing i got

Answer 19

6
--------------
6 | 46 92 25 6*6 =36

Answer 20

6
--------------
6 | 46 92 25 6*6 =36
+6 -36 I added 6+6 =12 on the left and subtracted 36 from 46
... -------
12 10

Answer 21

6?
--------------
6 | 46 92 25 6*6 =36
+6 -36 I added 6+6 =12 on the left and subtracted 36 from 46
... -------
12? 1092 I brought down next pair

Answer 22

Now think of a number ? which makes 12? X ? close to 1092

Answer 23

8

Answer 24

8

Answer 25

right

Answer 26

68
--------------
6 | 46 92 25 6*6 =36
+6 -36 I added 6+6 =12 on the left and subtracted 36 from 46
... -------
128 1092 I brought down next pair
+ 8 - 1024
-----------------------
136 68

Answer 27

68?
--------------
6 | 46 92 25 6*6 =36
+6 -36 I added 6+6 =12 on the left and subtracted 36 from 46
... -------
128 1092 I brought down next pair
+ 8 - 1024
-----------------------
136? 6825 i bring the next pair down and do the proces again

Answer 28

1365*5=6825

Answer 29

till I get 0 in the remainder

Answer 30

right

Answer 31

you got it...........so the answer is 685

Answer 32

great.... I got the process.
seen it for the first time.

Answer 33

what will we get if the number is not a perfect square???
the loop will never stop???

Answer 34

food for thought
68*69 = 4692

Answer 35

looks like we're finding sqrt for 46 00 00 first
next, subtracting 36 00 00
next, finding sqrt of 10 92 00
...
after that i lost a bit...

Answer 36

@ganeshie8 what we are doing is we are finding the maximum significant digit that can be in the square root of the given number.............then we find the next and so on

Answer 37

there is this cool thing about perfect squares ending in 25,
the last digit of square root is 5, ofcourse.

the remaining digits, leaving 25 can be expressed in the form n(n+1)
and the square root will be (n5)

example, 4225---->6*7=42---->(65)^2
15625---->12*13=156---->(125)^2

incase you guys didn't know.... :)

Answer 38

I've never seen this method either (or if I have, it was a very long time ago and I've forgotten it... lol). Fascinating. Thanks for the lessons @atlas . I want to study this a bit later when I have more time and really wrap my head around it. I get the mechanics, but I'd like to understand the theory around it better. :)

Answer 39

625 = 2(2+1), 5
= 25

cool trick ! @hartnn this works oly for perfect squares i think

Answer 40

yes, only for perfect squares ending in 25

Answer 41

for 725, we cant write it as n(n+1)

Answer 42

that trick is taken from a VEDIC math book.
many such trick are there, which makes calculations much much easier...

Answer 43

(n)*(n+1)*100+25
=(10n)^2 + 2* 10n * 5 +5^2
=(10n+5)^2

Answer 44

yup! i like VEDIC math :) i go thru once in a while.... somebody should write a book why/how VEDIC tricks works also (reasoning behind them)

Answer 45

=(10n+5)^2
=(n5)^2

Answer 46

^^ saura u should write a companion book for VEDIC math... it sells im sure :)

Answer 47

lol

Answer 48

hahaha

Answer 49

@ganeshie8 did you get the theory behind what atlas did?

Answer 50

not yet, thats not obvious to me at all.. i gave up after trying for sometime.
will get back to that in my evening ...

Answer 51

wbu saura ? it clicked to u?

Answer 52

no.... I am thinking on it

Answer 53

I think it is pretty straight forward......the method does the algebraic manipulation at the backend:
for the above example
(100x + 10y +z)^2 = 469225
10000x^2 + 100y^2 +z^2 + 2000xy + 20yz + 200xz = 469225

Answer 54

we can find the value of MSB (x) which should be 6 here because 7 gives us a no. greater than RHS:
So it becomes
100y^2 +z^2 +2000xy +20yz +200xz = 469225 - 360000

Answer 55

Again we add x+x (6+6) and keep it in ten's place.......i.e like 20x(120) and we think of a number y (8) that makes the number............20x+y(128) and we multiply this with y again making it 20xy + y^2

Answer 56

We are inherently multiplying this number 20x + y^2 with 100 because you see we are subtracting it with 1092(00).......so what we are doing is we are subtracting 2000xy + y^2 from RHS after getting the value of y

Answer 57

THis process continues