Tuesday, 16 May 2017

Approximation II – Approximation Questions on finding Cube Root of Imperfect Cubes

In this post, we will discuss approximation questions that are on finding cube roots of imperfect cubes
Approximation Questions

Finding cubes roots of imperfect cubes in SBI PO, IBPS PO and SSC CGL Exams is such a tough process. Numbers which do not have a perfect cube, it becomes challenging to find their approximate cube root.

In our previous post – Approximation I – Approximation Questions on finding Square Root of Imperfect Squares, we have solved approximation questions that are based on finding the square root of imperfect squares. In this post, we will solve find solutions to the approximation questions that are asked on finding cubes of imperfect cubes.

Example 4: Approximation questions on finding cube root of imperfect cube
                                                                      
Question: What is the approximate cube of 80000?

Solution:
Step 1:
 Find the nearest cube that is near to80000
403 = 64000
503 = 125000

Step 2:
Now we know that cube of 80000 lies between 40 and 50. We can mark any number that lies between 40 and 50 in the option and most probably a number which is close to 50. But there is a method through which we can find the cube root.

First, take the closest perfect cube to 80000 and subtract it from 80000.
I.e. 403 = 64000
80000– 64000= 16000

Then, as we need to find the approximate cube we add something to 40 i.e. the difference and divide it with the difference of the minimum and maximum approximation of perfect cube.
403 - 503= 64000 – 125000 = 61000
40 + 10 [64000/61000](multiply by 10)
40 + 10 x 0.25 = 42.5
So, you can mark the option that is close to 42.5

Therefore, the approximate cube of 80000 is 42.5. 
Approximation Questions
Example 4: Approximation questions on finding cube root of imperfect cube

Question: What is the approximate cube of 250000?

Solution:
Step 1:
Find the nearest cube that is near to250000
603 = 216000
703 = 343000

Step 2:
Now we know that cube of 216000 lies between 60 and 70. We can mark any number that lies between 60 and 70 in the option and most probably a number which is close to 70. But there is a method through which we can find the cube root.

First, take the closest perfect cube to 250000 and subtract it from 250000.
i.e. 603 = 216000
250000– 216000= 34000

Then, as we need to find the approximate cube we add something to 60 i.e. the difference and divide it with the difference of the minimum and maximum approximation of perfect cube.
603 - 703= 216000 – 343000 = 127000
60 + 10 [34000/127000] (multiply by 10)
40 + 10 x 0.25 = 62.5

So, you can mark the option that is close to 62.5

Therefore, the approximate cube of 216000 is 62.5. 

Find the cube root of the following approximate questions and drop in your answers in the comment section.

Question:.∛474548.98 = ?
1) 78         2) 68         3) 72               4) 76               5) 80

Question: ∛1519.985 = ?
1) 12.5      2) 9.5          3) 10.5            4) 11.5            5)11.4

Stay tuned for more approximation questions.
Approximation Questions
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