Aptitude - Square Root and Cube Root - Discussion

By hypothesis cube root of .000216=(0.000216)^1/3.
=[(216)/10^6]^1/3.
we know that 6^3=216
So( 6^3)^1/3=6
and ll'y (10^6)^1/3=(10)^2
So (216/10^6)^1/3=[(6^3/10^6)]^1/3
=6/10^2
=6/100.
So The cube root of 0.000216 =0.06.

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.

@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.

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?

The Easy method is (0.000216) means now you see in the cube numbers where the last digit 6 is coming.

6 is coming in 6 cubes the see after last 3 digits from the question that is zero, and finally, 0.06 is the answer.

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.

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.

Why divided 216 by 10(6) and after that 6*6*6
---------
10(2)*10(2)*10(2)
I cant understand this solution...

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.

@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?