Approximation I – Approximation Questions On Finding Square Root Of Imperfect Squares

In this post, we will discuss few approximate questions that are asked on finding square root of an imperfect square in IBPS PO, IBPS Clerk, SBI PO, SBI Clerk, SSC CGL, SSC CHSL and other competitive exams. The quantitative aptitude section of IBPS PO, IBPS Clerk, SBI PO, SBI Clerk, SSC CGL, SSC CHSL and other competitive exams, consists of a few approximation questions that we often tend to skip due to huge calculations. Approximation means a value or quantity that is nearly but not exactly correct. Generally, approximation questions are on finding the square root of imperfect squares, finding the cube root of imperfect cubes, simplification etc. Approximation questions are based on speed calculations and guesswork.
Approximation Questions are divided into various parts. In this post, we discuss approximation questions when they are asked on finding the squares root of imperfect squares in less time.
Example 1: Approximation questions on finding square root of imperfect squares

Question: What is the approximate square of 8000?
Solution:
Step 1:
Find the nearest squares that are near to8000
802 = 6400
902 = 8100
Step 2:
Now we know that square of 8000 lies between 80 and 90. We can mark any number that lies between 80 and 90 in the option and most probably a number which is close to 90. But there is still a method through which we can find the square root.
First, take the closest perfect square to 8000 and subtract it from 8000.
I.e. 80² = 6400
8000 – 6400 = 1600
Step 3:
Then, as we need to find the approximate square we need to add something to 80, so we add the difference and divide it by  double the number that is taken i.e. 80 x 2
80 + [1600/(2 x 80)] = 90
So, you can mark the option that has 90
Therefore, the approximate square of 8000 is 90.

Question: What is the square of 6000?
Solution:
Step 1:
Find the nearest squares that are near to6000
702 = 4900
802 = 6400
Step 2:
Now we know that square of 6000 lies between 70 and 80. We can mark any number that lies between 70 and 80 in the option and most probably a number which is close to 80. But, there is a method through which we can find the square root.
First, take the closest perfect square to 6000 and subtract it from 6000
I.e. 70² = 4900
6000 – 4900 = 1100
Step 3:
Then, as we need to find the approximate square we need to add something to 70, so we add the difference and divide it by double the number that is taken i.e. 70x 2
70 + [1100/ (2 x 70)] = 78
So, you can mark the option that has 78
Therefore, the approximate square of 6000 is 78.
Example 3: Approximation questions on finding square root of imperfect squares

Question: What is the square of √14000?
Solution:
Step 1:
Find the nearest squares that are near to14000
1002 = 10000
1102 = 12100
1202 = 14400
Step 2:
Now we know that square of 14000 lies between 110 and 120. We can mark any number that lies between 110 and 120 in the option and most probably a number which is close to 120. But, there is a method through which we can find the square root.
First, take the closest perfect square to 14000 and subtract it from 14000
I.e.110² = 12100
14000 – 12100 = 1900
Step 3:
Then, as we need to find the approximate square we need to add something to 110, so we add the difference and divide it by double the number that is taken i.e. 110x 2
110 + [1900 / (2 x 110)] = 119
So, you can mark the option that has 119
Therefore, the approximate square of 14000 is 119.
Do write down in the comment section how this post helped you to solve approximation questions on finding square roots of imperfect squares.Stay tuned for more approximation questions.  Recent comment authors 