# Aptitude - Square Root and Cube Root - Discussion

### Discussion :: Square Root and Cube Root - General Questions (Q.No.4)

4.

1.5625 = ?

 [A]. 1.05 [B]. 1.25 [C]. 1.45 [D]. 1.55

Explanation:

```   1|1.5625( 1.25
|1
|-------
22| 56
| 44
|-------
245| 1225
| 1225
|-------
|    X
|-------
``` 1.5625 = 1.25.

 Varun said: (Jul 24, 2010) We can write it as 15625/10000. 5 power of 6 is 15625 and it becomes 5 power of 6/10 power of 4.. 125/100=> 1.25

 Abinash said: (Jul 29, 2010) Well I think in the 3rd step it should be something after 22 not 24..yes or no? if 245 then how?

 Deepti said: (Aug 1, 2010) Varun's explanation is easier to under stand.

 Abdul said: (Sep 29, 2010) Can you please tell how 125/100?

 Rajesh said: (Dec 16, 2010) the power 6 and power 4 get cancel. then we have 5 power 3 and 10 power 2.

 Sandeep said: (Jan 25, 2011) Actually, 225 = 15*15 = 1*2 625 = 25*25 = 2*3 1225 = 35*35 = 3*4 So... 15625 = ????? = 12*13 = 12*12 Hence it'll be 125/100 = 1.25

 Shri said: (Feb 27, 2011) Anyone can explain varun's 3rd step?

 Sakshi said: (Mar 2, 2011) Hi Shri! 5 power of 6 and 10 power of 4 we can write it= 5 square*5 square*5 square/10 square*10 square under root it will bcome 5*5*5/10*10 =125/100 =1.25

 Shalini said: (Jun 17, 2011) 15625 we can distributed in two parts like 156/25 becouse we calculated the sqaure any number were ends digit is 5 the last digit of answer is always 5. now camo to second part of d no. square of 12 is 144and square of 13 is 169. square of 13 is > 156 so that we took 12 now we get "125" is the right ans.

 Abhay said: (Jun 24, 2011) Sakshi...U r the Best!! Awesome... Thnks Too...good

 Rakshit said: (Jul 26, 2011) @Sakshi is this method works for all numbers that has the last digit as 5 ?

 Anila said: (Aug 6, 2011) ((5^6)1/2)/((10^4)1/2)=5^3/10^2=5*5*5/10^2=125/10^2=125*10^-2=1.25

 Arun.G said: (Sep 5, 2011) I'm not understand the answer 1.25 according to me we divided 1.5625 the answers are 1, 22, 245 how 1.25 comes.

 B.Sridhar said: (Oct 1, 2011) Shalini explanation is good but the number is different that is 17079 how to calculate please tell me.

 Kiran said: (Oct 27, 2011) Varun explaination is very good.

 Murali said: (Nov 25, 2011) root of 1.5625 = ? We can write it as 15625/10000. =1.5625 = root of 1.5625 = 1.25

 Ranjeet said: (Jan 8, 2012) How instantly get 5 power of 6 = 15625 as explained by Varun initially, is there as short formula please explain any one ?

 Sandhya said: (Mar 29, 2012) sqrt of 1. 5625 = sqrt of [15625/10000]. 15625=125*125 ; 10000=100*100. =125^2 ; =100^2. sqrt of 15625=[125^2]^ (1/2) ; sqrt of 10000=[100^2]^ (1/2). Powers get cancelled, therefore = 125/100. = 1. 25.

 Hari said: (Apr 9, 2012) Hi friends, I can't to understand how to take square root from any number. Could any one explain me please.

 Dipankar said: (Apr 22, 2012) Tricky:for Square root separate them in 2 parts from the right hand side i.e. 1089 like 10/ 89. 1st we hav find out root of last digit 9 is 3. 2nd we need 2 look4 the nearest square of 10 is 3. So your answer come 33. More: 3249. 1st:32/49. 49's root is 7 & nearest square of 32 is 5 (25). So answer be 57.

 Krishna Teja said: (Aug 27, 2012) @Dipankar. Thank you very much dude :).

 Kumari said: (Sep 2, 2012) @Dipankar Nice Trick dipankar. Please keep sharing your knowledge..thanks!

 Dinesh Kumar said: (Feb 9, 2013) 5| 15625 ---------- 5| 3125 ---------- 5| 625 ---------- 5| 125 ---------- 5| 25 ---------- 5| 5 ----------- So 5*5* 5*5* 5*5 get each one 5*5*5=125. 5 1.5625 after the point we have four(2*2)digit. So put the point before two digit 1.25 is the answer.

 Shali said: (Apr 28, 2013) 5 | 15625 ---------- 5 | 3125 ---------- 25| 625 ---------- 25| 25 ---------- | 1 5*5*25*25 while taking square root 5*25 = 125 i.e 1.25 decimal after 2 digits.

 Shruti said: (Jun 6, 2013) @Dipankar. In the case of 1089 you found out the root of last digit i.e. 9 but in case of 3249 you did calculate the root of last two digits i.e.49 instead of the last digit only i.e. 9. Isn't it contradicting each other?

 Imran Khan said: (Jul 29, 2013) Let me know how can we understand 22 is to come or 245 in particular steps?

 Lithin said: (Aug 5, 2013) Can anyone please explain the factorization method?

 Dulberg said: (Oct 10, 2013) @Shruti. I think @Dipankar was just trying to give a clue. Personally I find it very useful. It gives you the idea about the figure you should expect.

 Priya said: (Mar 7, 2014) We can write 1.5625 as 15625/10000. So, (125)^2=15625 and (100)^2=10000. So, by taking square root of this it became 125/100 So the answer is 1.25.

 Oshin said: (Apr 1, 2014) Ya its 1.25, one method is. Take last 2 digits 25, and square root of it is 5. And 156 = 12*13, we must take smaller number, 12. So its 125 and add decimal, then its 1.25.

 Sai Prasanna said: (Jul 7, 2014) We can easily calculate by given options i.e., 1.25 * 1.25 = 1.5625.

 Vivek Wadhawan said: (Aug 30, 2014) @Dipankar. Your trick is good but didn't work for square of n. O whose digit ends with 7. Let me give an example. 77^2 = 5929. That means acc to your trick sqrt of 5929 should be 73. Where it fails. Another ex :- 27^2.

 Amisha said: (Sep 7, 2014) sqrt(15625/10000) Now for 15625, separate into 156 and 25. For 156, divide into two consecutive number i.e 12*13 and choose least number i.e. "12". For 25, square root is "5". Now combine both i.e. 12 and 5 which makes "125". Now, 125/100 gives 1.25. This is true for any which can fulfill the criteria i.e. 1. Consecutive number and choosing lower of both. 2. Last 2 digits 25. This method is best when you know that the number is a perfect square.

 Raj said: (Sep 23, 2014) Can you explain in more simpler manner?

 Parthkushte said: (Jan 9, 2015) Whenever a sq.rt. ends with "25"(1.56'25'), the last digit of root is always "5"(1.25). The other 'digits can be found by this method: '12'X'13' = '156('1.56'25).

 Rakshit said: (Feb 27, 2015) In main solution there is 225 instead of 245 might be.

 Anil said: (Apr 21, 2015) Can any one tell why 22 and 245 came in solution they give in the explanation?

 Prashant said: (May 18, 2015) 1.25 --------------- 1*1| 1.5625 +1| 1 ---------------- 22*2|056 +2|044 |- ---------------- 245*5|1225 1225 -------------- 0000 So answer is 1.25. So that is the region, why we take 22 and 245.

 Sheetal said: (Jul 30, 2015) Thanks for the simple explanations. Please include shortcut tricks along with the explanations.

 Rkcckr said: (Aug 16, 2015) 1.5625 = 15625/1000. N Numerator = 5^2*5^2*5^2. D Denominator = 10^2*10^2. Square root of N/D = 5*5*5/10*10 = 125/100 = 1.25.

 Som said: (Dec 29, 2015) Remember trick, in 15625 last two digits can be obtained by multiplying 5*5. Now 156 can be obtained by multi 12*13. So answer will be 125 now put decimal accordingly.

 Siva said: (Feb 23, 2016) 1.25 *1.25. If the last digits ends with 5 always in both the sides multiply 5*5. Then in the first digit add one number. 12 + 1 = 13. Now multiply 12*13 = 156. This method will be more easy.

 Jay said: (Mar 10, 2016) From the above explanation We get the answer square root of 15625 = 125. Now in the question the decimal digits are 4. So in the answer we should have 4/2 = 2 digits in decimal after point so answer is 1.25.

 Laks said: (May 25, 2016) @Shalini and @Dipankar Your method is Right.

 Rudh said: (Jul 18, 2016) @Sandhya. Thank you so much.

 Kiran said: (Aug 8, 2016) Thank you friends. It is easy to understand now.

 Sidhu said: (Jan 21, 2018) @ALL. Very simple short cut 1+5+6+2+5 = 8 [A]. 1.05(1+5)=6. [B]. 1.25 (1+2+5)=8. [C]. 1.45(1+4+5=10)=(1+0)=1. [D]. 1.55(1+5+5=11)=(1+1)=)2. So the answer is B.

 Rahul said: (Dec 1, 2018) @Varun The 3rd step is; {(5*5*5*5*5*5)/10*10*10*10)}, = 5*5*5/10*10, = 125/100, = 1.25.

 Hareesh said: (Jan 17, 2019) (15625/10000)^0.5. = (15625^0.5)/{10^(4/2)}, = {(5*5*5)(5*5*5*)}^0.5/(10^2). = 125/100, = 1.25.

 Pranitha said: (Feb 11, 2019) (15625/10000) ^1/2. We have to cancel the above 2values. Then we get (25/16) ^1/2, = 5/4. The ans is 1.25.

 Rahul said: (May 15, 2019) @Sidhu. How is 1+5+6+2+5=8?

 Honnu said: (Jun 6, 2019) @Sidhu. 1+5+6+2+5=19, How it will be 8? Please explain.

 Karthick said: (Jun 14, 2019) Thanks for explaining the answer @Varun.

 Swetha said: (Aug 23, 2019) Let we know x2 = a. So, x = √a. Therefore by referring to all the options with there square; Let options A)1.05 * 1.05 = 1.1025 B)1.25 * 1.25 = 1.5625. So by this, we recognise option B is correct.