Aptitude - Square Root and Cube Root - Discussion

What is square root of 1764/2 and how?

To know how division method works:

2|64009( 253
|4
|----------
45|240
|225
|----------
503| 1509
| 1509
|----------
| X
|----------
---------------------------------------------------

2|64009( 253
+2|4
--|----------
45|240
+5|225
--|----------
503| 1509
| 1509
|----------
| X
|----------

For those who wanted to know about the 2, 45, 503...

1. Take the number(64009) and divide in pairs from lhs to rhs starting from unit digit.
i.e., <------ 64009==> 6 40 09.

2. Then start the division by finding perfect square lesser than the number(6).
2sq = 4<6.
3sq = 9>6.
Hence choose 2.

3. To know how 45 came as next divisor take previous divisor 2 and add 2 ===> 4x.
> 4x 4 is the first digit.
> 4x x next digit to be choose from trail and error again such that this and quotient remains the same.

41*1=41<240.
42*2=84<240.
43*3=129<240.
44*4=176<240.
45*5=225<240.
46*6=276>240. // so choose the previous no. i.e. 45.

Hence choose 45.

4. To know how 503 came as next divisor. Take previous divisor 45 and add 5 ===> 50x follow the same procedure again.
503*3 = 1509.
:)

14713, 69
1 for 9 --- last digit should be 3 or 7.
2 so next 14713 nearest square is 121.
3 next 121*122=14762>14713 so take 3,

4 answer is 1213.

Suppose 1437601.
1 for 01 --- last digit should be 1 or 9.
2 so next 14376 nearest square is 119=14161.
3 next 119*120=14280<14376 so take 9,

4 answer is 1199.

How we find the square root of 7 digit no(1471369) ? Please explain.

How to find a given number is perfect square?

2|64009( 253
|4
|----------
45|240
|225
|----------
503| 1509
| 1509
|----------
| X
|----------
64009 = 253.

what is the process for above calculation?

Value of : square root of (3+root 5) is equal to ?

1) squareroot(3)/2 + 1/squareroot(2).
2) squareroot(3)/2 - 1/squareroot(2).
3) squareroot(5)/2 + 1/squareroot(2).
4) squareroot(5/2) + squareroot(1/2).

Tell me the answer with explanation please or send it to me.

Please tell me. This method is applicable to square of any number or not ? and tell me the any limitations are there in this method where this method can not use ? if yes then inform.

Give answer (explain me) -> square root of 659847. 56845=?

I mean how to distribute this number in two-two parts before and after the point?

Guys it's very simple to find the Square root of 5 digits no. just follow this method.

64009 there are 5 digits.

First take first 3 digits, in our case it's 640.

Now find the nearest square of 640. It is 625 which is 25^2 (it should always be less than our no.)

Here, we found 25 which are the first 2 digits of our Answer. now we have to find remaining digit.

Next step we have to double the 25. So it is 50. keep this 50 separate.

Now minus 625 out of 640, the reminder is 15. Like below:

Now 64009
625
------
1509


Then remaining would be 15 and 09 so it becomes 1509 when you joint them together.

Now consider the number which is in unit place from 1509.

In our case it is 9 (Note:- remember 9 always comes when you square 7 (49) and 3 (9))

So now always go for smaller no. of 7 and 3.

We take 3 which is smaller.

Now Join this 3 with 50 (which we double the 25).

Like this it becomes 503 and multiple this 3 with joined digits like this 503*3

It becomes 1509.

So the digits in final should be similar to the above reminder of 1509 ( and it would always be similar).

So this 3 is Last digit of our answer.

First 2 digits we had already found in the beginning which is 25.

So join them respectively,

So answer is 253.

@Lokesha.

Subtract the number 10817 with 1.

10816 is perfect square of 104.