Aptitude - Square Root and Cube Root - Discussion

@ Amar

In the same way how we can find the square root of 737881 ?

What number we will take into first consideration ? 7 or 73 ?

If 7 it will be 2 (2*2). -> leads to mistake.
if 73 it will be 8 (8*8) -> leads to correct answer.

@Rafeek

Count the digits of the given number.
If it is odd take only the first number,
If it is even take first and second number for first consideration.

In this example the number 64009 is a 5 digit number. 5 is odd number. So take only 6 for first consideration.

Is there any such method 2 find the cube root without finding the factors ?

How 45 and 503 came in this problem please add more similar problems with explanation?

Why we should not multiply with 3 at the first step of above procedure 3)64009(2.

Why we should not multiply with 3 at the first step of above procedure 3)64009(2. I need brief explanation ?

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.

1. Pair 6 40 09, subtract 6 by largest square number which is less than 6.

2. The number is 2(2*2=4),

The square of 64009 starts from 2XX, Hence answer is 253.

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.

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.