Aptitude - Square Root and Cube Root - Discussion

Discussion :: Square Root and Cube Root - General Questions (Q.No.1)

1. 

The cube root of .000216 is:

[A]. .6
[B]. .06
[C]. 77
[D]. 87

Answer: Option B

Explanation:

(.000216)1/3 = 216 1/3
106

   = 6 x 6 x 6 1/3
102 x 102 x 102

   = 6
102

   = 6
100

   = 0.06


Murali said: (Dec 4, 2010)  
Its wrong it is .006

Sakshi said: (Mar 2, 2011)  
Hey Murali! you are confused. Have a look.

We write 6/10= 0.6, 6/100= 0.06.

Its clear.

Rose said: (Mar 4, 2011)  
Ya correct.

Naseer said: (Mar 5, 2011)  
See guys the simple technique is just watch the last digit i.e 6.

Now multiply the last digit in the options that should be tally with the last digit in the question.

Now observe total no of zeroes after .(decimal)

Got it?

Afrin said: (Jun 7, 2011)  
Why divided 216 by 10(6) and after that 6*6*6
---------
10(2)*10(2)*10(2)
I cant understand this solution...

Afrin said: (Jun 7, 2011)  
Why 6/10 (2) ?

Pravin Raj said: (Jul 31, 2011)  
Obviously its corret.

Sangeetha said: (Aug 14, 2011)  
Naseer please can you elaborate your solution.

Chandu said: (Sep 2, 2011)  
Is there any shortcuts for finding cube roots and square roots? It there please tell me.

Namrata said: (Sep 15, 2011)  
Always keep in mind that a cube root of six digit number is two digit number so cube root of .000216 is .06 and not .6.

Ravi said: (Oct 26, 2011)  
Thanks namrata.

Mark said: (Nov 6, 2011)  
Thanks namarta.

Murali said: (Nov 25, 2011)  
6/102 can you people explain me how you got this step?

Narender said: (Nov 29, 2011)  
Could tell me simple principle for this method ?

Jyothis said: (Jan 5, 2012)  
It is a simple problem
(0.000216)= (216/10^6)
(216/10^6)= ((6*6*6)/(10^2*10^2*10^2))
By taking the cube root now
((6*6*6)/(10^2*10^2*10^2))^(1/3)= (6/10^2)
6/100=0.06ans

Vikas said: (Oct 17, 2012)  
Why we get 1/3?

Parul said: (Oct 27, 2012)  
Because cube root is equal to 1/3.
Like : cube root 9 is equal to 9^1/3.

Got it. Vikas.

Siva said: (Dec 11, 2012)  
Please tell me friends is there any short cut find cube root.

Anil said: (Jul 22, 2013)  
Easy method:

0.000216 = [216/10^6].

[0.000216]^1/3 = [216/10^6]^1/3.

= [6^3/10^6]^1/3.

= [6/10^2].

= 6/100=0.06.

Raaz said: (Aug 28, 2013)  
It is a simple problem:

(0.000216) = (216/10^6).

(216/10^6) = ((6*6*6)/(10^2*10^2*10^2)).

By taking the cube root now.

((6*6*6)/(10^2*10^2*10^2))^(1/3) = (6/10^2).

6/100 = 0.06 Answer.

Sridhar said: (Aug 29, 2013)  
How to get 1/3?

Chandini said: (Sep 6, 2013)  
@Sridhar.

Actually square root means 1/2 and cube root means 1/3.

We should find the 1/3 of 0.000216.

To eliminate point and 0's we should need 10^6 so it is.

216/10^6 = ((6*6*6)/(10^2*10^2*10^2))1/3.

= ((6^3)/((10^2)^3)).

= 6/10^2 = 6/100.

= 0.06.

Nathaniel said: (Jan 12, 2014)  
I don't understand how you got 6\10^2 please I need a better explanation from that point.

Shreya said: (Mar 10, 2014)  
0.000216 just take the cube for 216.

216 is the cube root of 6.

After the decimal point we have three zeros.

i.e. 216/1000 so every two zero we should consider one zero its come like this 0.06.

Yogi said: (Mar 30, 2014)  
0.000216 you underline to three digit.
right to left,
one is 216.

other is 000.
Answer is 0.06.

Chandan said: (Apr 2, 2014)  
Very sort method.

(216/10^6)^1/3 = (6^3/10^6)^1/3.
= 6^3*1/3/10^6*1/3.
= 6/10^2 = 6/100 = 0.06 Answer.

Ranjini said: (May 8, 2014)  
@Yogi I can't understand please give a brief explanation for solve it. And one thing I don't know the formulas so please help me.

Swati said: (Jun 7, 2014)  
Can you elaborate method to find multiple of 216?

Mohd Aquib Ansari said: (Jun 16, 2014)  
Hey Ranjini, there is no formula to use in this problem.

See here carefully,
we write 2/10 = 0.2.
3/10 = 0.3.
4/10 = 0.4.
And so on..

2/100 = 0.02.
3/100 = 0.03.
4/100 = 0.04.
and so on...

So we can write,
216/1000000 = 0.000216.

And know that,
216/1000000=6*6*6/100*100*100.

So we can say that,
The cube root of 0.000216.
or 216/1000000 = 6/100 = 0.06.

Swathi said: (Sep 20, 2014)  
0.06.

It is a simple num so easy to find. For large num how to find ? please tell me any simple way if any body know.

Sangita said: (Nov 5, 2014)  
But how guess the 216 is obtain by 6*6*6....?

Simmu said: (Nov 8, 2014)  
@Sangita.

Remember that very simple 1^3=1, 2^3=8, 3^3=7, 4^3=4, 5^3=5, 6^3=6, 7^3=3, 8^3=2, 9^3=9.

So 216 unit digit is 6 so guess 6^3=216.

Raimat said: (Dec 13, 2014)  
@Mohd Aquib, thanks for the straight explanation.

Iyappan31 said: (Mar 1, 2015)  
How can we us convert 216 in to 6?

Aparna said: (May 25, 2015)  
Hi actually 10^6 how you took give me proper explanation?

Pradad said: (Oct 20, 2015)  
Hi, Can you find solution for that in different manner which saves time for us?

Naik said: (Oct 31, 2015)  
Can you explain short cut in this topic?

Arun said: (Nov 4, 2015)  
That sum is totally confused.

Vikas said: (Jan 3, 2016)  
Thanks to all I got more knowledge about maths. And I request you to all made me understand about how to solve fraction please.

Madhavi said: (Feb 18, 2016)  
Friends, I can't understand it.

1^3 = 1, 2^3 = 8, 3^3 = 7, 4^3 = 4, 5^3 = 5, 6^3 = 6, 7^3 = 3, 8^3 = 2, 9^3 = 9.

Can someone explain please?

Deepika said: (Apr 19, 2016)  
@Madhavi
1^3 = 1
2^3 = 8
3^3 = 27 the unit digit is taken into consideration i.e 7.
Similarly,
4^3 = 64 the unit digit is taken into account i.e 4.

And so on... Is it fine now?

Hari said: (Jul 11, 2016)  
A simple method, just multiplies the options 3 times we will get the answer.

Which means, 0.06 * 0.06 * 0.06 = 0.000216, we know it is impossible to get an answer from option C and D.

Jitendra said: (Jan 7, 2017)  
0.06 * 0.06 = 0.006.

And also,
0.006*0.06 = 0.0006.

Nimisha said: (Apr 20, 2017)  
Can't understand the solution. Can anyone help me?

Harrsha said: (May 24, 2017)  
How the denominator is 10^6? Please explain.

Sayedul Si said: (Jun 16, 2017)  
How to get 216/106?

Narsimha Reddy said: (Jul 1, 2017)  
I Didn't get it. Please, Help me.

Sahil Jaiswal said: (Aug 29, 2017)  
It's simple last digit of no is six then I take no six nd three no cancel then I have only.000 so it right to =0.6.

Shrishti said: (Mar 13, 2018)  
Can't understand. Please help me.

Ujwal Chinta said: (Jun 22, 2018)  
Can't understand this. Please, someone explain me.

Reshma said: (Oct 2, 2018)  
6*6*6 = 196 how can it be 216 here?

Randyranjith said: (Oct 8, 2018)  
Can't understand.

Abhinav said: (Oct 29, 2018)  
Thanks, I understand the solution clearly.

Priyanka said: (Feb 20, 2019)  
Thank you all for the given explanation.

Kirthana said: (Mar 28, 2019)  
@Reshma, the cube of 6 is 216. Not 196.

And, how is it 0.06? what should we do?
please, anyone, explain me.

Ankush said: (May 1, 2019)  
Yes, it is 0.006.

Chhaya said: (Jul 21, 2019)  
I can't understand how come 6/10^2? please help me.

Yogi said: (Sep 15, 2019)  
I am not understanding it. Please, anyone explain it for me.

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