In this chapter we will learn to find square root of numbers which are not perfect square.
We have already discussed factorization and long division method of square root calculation. Please understand those chapters first before moving on with this post.
What are non perfect square ?
The numbers whose square root is not a whole number are termed as non perfect square.
Numbers like 7, 11, 15, 17 etc. are some of the examples of non perfect square.
Calculate square root of non-perfect square ?
Remember that square root of some non – perfect squares are decimal numbers whose values go on and on.
In this case you have to find approximate value of the numbers.
Follow the below steps to calculate the square root;
(a) Use long division method to calculate the square root.
(b) If you are asked to calculate answer up to n decimal places then;
(i) Calculate the square root up to (n + 1) decimal place.
(ii) Check the digit in (n+1) decimal place.
⟹ If digit is < 5, keep the nth digit same.
⟹If digit is > 5, then increase nth digit by 1.
I hope you understood the above process. Let us solve some examples for further clarity.
Example 01
Find square root of 6 up-to 2 decimal places.
Solution
Since the question is asking for solution up to 2 decimal places, we will first calculate the square root up to 3 places after decimal.
Calculating square root using long division.
we get 2.449 is the approximate square root.
Since we have to find the solution up-to 2nd decimal place, check the digit in 3rd decimal place.
3rd Decimal place = 9
Since 9 > 5, we will increase the 2nd decimal place by 1.
Hence, 2.45 is the solution of given problem.
Example 02
Find the square root of number 13 up – to one decimal place.
Solution
Use the long division method to find square root of given number.
Since the question is asking for 1 decimal place solution, we have to do the calculation till 2nd decimal place.
Here we get 3.60 as the square root of 13.
2nd decimal place digit ⟹ 0
Since 0 < 5, the digit in 1st place will remain the same.
Hence, 3.6 is the square root of given number.
Example 03
Find square root of 1.5 up to second decimal place.
Solution
We will use long division method to find square root.
Since the question is asking for solution up to 2nd decimal place, we will have to solve the long division till we find 3rd decimal place number.
So 1.224 is the square root of given fraction.
Since, the question is asking for solution up to 2nd decimal place, let’s check the number in 3rd place.
Digit in 3rd place = 4
Since 4 < 5, we will not change the 2nd decimal place digit.
Hence, 1.22 is the required solution.
Example 04
Find the square root of 24 up to one decimal place.
Solution
Solving using long division method.
Here we got 4.89 as the solution.
Since we have to find square root till one decimal place, let’s check the digit in 2nd decimal place.
2nd decimal place number = 9
Since 9 > 5, we will increase the first decimal place by one.
Hence, 4.9 is the solution.
Example 05
Find the square root of 5.8 up to second decimal place.
Solution
Using long division method.
Here we got 2.408 as solution.
Since, we need the value up to 2nd decimal place, let’s check the digit in 3rd decimal place.
3rd decimal place = 8
Since 8 > 5, we will increase 2nd decimal place by 1.
Hence, 2.41 is the solution.