Aptitude - Square Root and Cube Root - Discussion

Step1 : Group the pair of digits from right side(unit place). The three groups are 6,40,09.

Step2 : Find the Largest square number less than or equal to the first group (6).

Since 3^2>6 and 1^2<6. 2^2=4 is the number.

Step 3 : Take the square root of 4 = 2

Step 4: Place 2 as quotient above the first group,

Step 5 : Place 2 also as divisor

Step 6 : Subtract from the first group (9), the product of divisor and quotient=4(=2*2) :The reminder is 2(6-4).

Step 7 : Consider this remainder and the second group (=440) as the new dividend.

Step 8 : Add divisor and the digit in the unit place of divisor.(2+2= 4). Find a digit x such that 4x multiplied by itself(x) gives a number < or = the new dividend (=240). We find that 45*5 = 225 which is less than the dividend 240. Therefore x=5. 45 will be the new divisor. Write 5 above the second group at the top.

Step 9 : Subtract 225, the product of this new divisor(45) and 5 from the dividend 240 - 45 *5 =15

Step 10: Consider this remainder (15) and the next group (09) as the new dividend (1509)

Step 11: Add divisor and the digit in the unit place of divisor.( 45+ 5= 50).Find a digit x such that 50x multiplied by itself(x) gives a number < or = the new dividend (=1509). We find that 503*3 = 1509 which is equal to dividend. Therefore x=3. Write 3 as quotient above the third group at the top.

Step 12 : Subtract 1509, the product of this new divisor(503) and the quotient 3 from the dividend 1509 -503*3 =0

Step 13 : Continue this process till there are no more groups for division.

We stop the process here as there are no more groups remaining for division.

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.

Simple trick:

Step-1: Look at the magnitude of the "hundreds number" (The numbers preceding the last two digits) and find the largest square that is equal to or less than the number. This is the 1st part of the answer.

Step-2: Now, look at the last (unit's) digit of the number. If the number ends in a:

0 -> then the ending digit of the answer is a 0.

1 -> then the ending digit of the answer is 1 or 9.

4 -> then the ending digit of the answer is 2 or 8.

5 -> then the ending digit of the answer is a 5.

6 -> then the ending digit of the answer is 4 or 6.

9 -> then the ending digit of the answer is 3 or 7.

To determine the right answer from 2 possible answers (other than 0 and 5) , mentally multiply the findings in step-1 with its next higher number.

If the left extremities (the numbers preceding the last two digits) are greater than the product, the right digit would be the greater option (9, 8, 7, 6) and if left extremities are less than the product, the right digit would be the smaller option (1, 2, 3, 4).

64009 - First does square of 25 which is 625 i.e. answer 25. Then does 25*26 = 650 640 < 650. So take smallest digit as per rule answer i.e 3.

Combine 25 and 3.

So answer is 253.

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.
:)

Hi, I am showing you short tricks for it. Read it carefully.

Firstly try to learn square root from 1 to 10 atleast. Like, 1=1, 4=2, 9=3, 26=4, 25=5, 36=6, 49=7, 64=8, 81=9, 100=10.

Then make pair of no given in question like, 64009 = 640 09, look at the last pair i.e. 09. And check square root which I have mentioned above, that which unit no showing unit digit of 9, so we got the nos are 3, 7.

Because square of 3=9, 7=49.

Now look at the first pair i.e. 640 and check which number of square root comes between 640, we got 25, 26 because 25*25 = 625, 26*26 = 676.

Now multiply lowest no between 25 and 26 to its successor i.e. 26.

25*26=650. We are confirmed that first to no will confirmly comes under our answer.

Now check 650 which calculated by 25*26 is greater or less by our first pair i.e 640. If 640 < 650 then unit digit of answer will be 3 otherwise unit digit will be 7.

So we got unit digit 3. And also kept 25, so 25 and 3 becomes 253. This is the short tricks use once. We will get square root of every digit by this. Have a great time.

First you should know that,
Square of any two digit number.

Means 20*20 = 400, 99*99 = 9801.

Here we get 3 digit in 20^2 & 4 digit in 99^2.

Now,

Ex. We want to find square root of no 5625.
Take first two digit 56,

Find no whose square is nearest to 56, no is =7
56 nearest to 49

So first digit is 7 of root of 5625 numer.
Now take second two digit 25.
Now take no whose square is is end with 5.

5^2 = 25 15^2 = 225. but as from earlier we know it is two digit no whose square is 5625. so we have to take 5, so second digit is 5.

So 5625 = 75^2.

Ex. Take 64009.
Take 640 nearest square no 25^2 = 625.
So first digit is 25.

Now take 09 it is end with 9.
So second digit is 3.

So 64009 = 253^2.

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?

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.

Ex- Take 64009.

Divide the no with two parts i.e 640 & 09.

As 9 is the last no, so it can be 3 or 7.

As 25^2 <640< 26^2.

Hence the no may be 253 0r 257 ( take the small number).

So 25*26=650..as 650>640. So we have to take the small number.

Hence the answer is 253.

In this problem, we take first three digit i mean 640 the well before the square no is 625 which is 25 square. Then the last digit is 9, clearly ending 9 reveals that it is 3 or 7. For clarifying this do square of 255 we get 75025. It obviously tells that the answer is 253.