Hi,
I have this problem written down in my notes & I still don't understand it.
Can you help?
"/" = radical sign
and the three should be a cube sign
/3/0.000064
GMAT Forum
4 postsPage 1 of 1
- Harish Dorai
Katherine:
There is an easy way to solve this by converting the decimal using exponents. Also recognize the number 64 in the decimal and as you know 64 is 4^3 (Read ^ as the "to the power").
As you know 0.1 can also be written as 10^ (-1), similarly 0.001 is 10^-3. Now to complicate things, we can say 0.0002 as 2 x 10^(-4). This is because 0.0002 can be interpreted as 0.0001 x 2 and 0.0001 is 10^(-4). Similarly 0.00012 will be 1.2 x 10^(-4).
Now coming to our problem. Let us first take the number 0.000064 can convert it into exponents.
0.000064 is actually 6.4 x 10^(-5). Now since you know 64 is the cube of 4. We can rewrite as 6.4 as 64 x (1/10) which is 64 x 10^(-1). The reason why I convert 6.4 using 64 is because I know 64 is a cube of 4 and hence it will be easy for us to find the cube root of 64 which is 4 (this is the last part of our problem)
So replacing 6.4 in the above exponent statement, we get 64 x 10^(-1) x 10^(-5). This will simplify to 64 x 10^(-6)
Now we need to find the Cube Root of 64 x 10^(-6).
The Cube of 10^2 is 10^6. Similarly the cube of 10^8 is 10^24. This is using the exponent theorm
A^m^n = A^(mn).
Now take 64 x 10^(-6) and try to find the cube root. You should know that Cube Root of (A x B) is Cube Root of A X Cube Root of B.
So to find Cube Root of 64 x 10^(-6), find the individual cube roots which is 4 x 10^(-2), which is 0.04.
So the answer to the problem is 0.04.
I understand it is a bit lengthier explanation. But I am doing it purposely to expose the different numerical concepts behind this. Especially numbers and roots get tricky with decimal numbers and we have to manipulate it correctly. With little bit of practice you can definitely master the concepts and do problems like this very quickly.
Good luck!!
There is an easy way to solve this by converting the decimal using exponents. Also recognize the number 64 in the decimal and as you know 64 is 4^3 (Read ^ as the "to the power").
As you know 0.1 can also be written as 10^ (-1), similarly 0.001 is 10^-3. Now to complicate things, we can say 0.0002 as 2 x 10^(-4). This is because 0.0002 can be interpreted as 0.0001 x 2 and 0.0001 is 10^(-4). Similarly 0.00012 will be 1.2 x 10^(-4).
Now coming to our problem. Let us first take the number 0.000064 can convert it into exponents.
0.000064 is actually 6.4 x 10^(-5). Now since you know 64 is the cube of 4. We can rewrite as 6.4 as 64 x (1/10) which is 64 x 10^(-1). The reason why I convert 6.4 using 64 is because I know 64 is a cube of 4 and hence it will be easy for us to find the cube root of 64 which is 4 (this is the last part of our problem)
So replacing 6.4 in the above exponent statement, we get 64 x 10^(-1) x 10^(-5). This will simplify to 64 x 10^(-6)
Now we need to find the Cube Root of 64 x 10^(-6).
The Cube of 10^2 is 10^6. Similarly the cube of 10^8 is 10^24. This is using the exponent theorm
A^m^n = A^(mn).
Now take 64 x 10^(-6) and try to find the cube root. You should know that Cube Root of (A x B) is Cube Root of A X Cube Root of B.
So to find Cube Root of 64 x 10^(-6), find the individual cube roots which is 4 x 10^(-2), which is 0.04.
So the answer to the problem is 0.04.
I understand it is a bit lengthier explanation. But I am doing it purposely to expose the different numerical concepts behind this. Especially numbers and roots get tricky with decimal numbers and we have to manipulate it correctly. With little bit of practice you can definitely master the concepts and do problems like this very quickly.
Good luck!!
4 posts Page 1 of 1