# Aptitude - Square Root and Cube Root - Discussion

Discussion Forum : Square Root and Cube Root - General Questions (Q.No. 15)
15.
The square root of 64009 is:
253
347
363
803
Explanation:
```   2|64009( 253
|4
|----------
45|240
|225
|----------
503|  1509
|  1509
|----------
|     X
|----------
```

64009 = 253.

Discussion:
41 comments Page 1 of 5.

Deepak said:   7 years ago
Good job, Thanks @Sakshi.
(2)

Raghvendra gupta said:   7 years ago
64009 from getting square root method only starting no.2 is perfect square 4 that is less than 6(64009).

So it must be noted that 1st digit must be less than 6 but the perfect square of 3 exceeds (6) and at lastno means 9 shows that last digit must be 3.

Aayush said:   7 years ago
Find the cube root of 176.
(4)

I want a simple explanation for this problem. Please provide it for me.

Maruti said:   8 years ago
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.

Deepika said:   8 years ago
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.
(3)

SUBHAJIT RAY said:   8 years ago
Why this kind of time consuming solution done?

First of all there are only 4 option. Simply multiply 363*363 then 253*253. Then we can see 253*253 will make 64009.
(2)

Waris said:   9 years ago
Anyone help me.

Waris said:   9 years ago
How is it possible its coming 263?

Pooja said:   9 years ago
I can't understand.