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Square Root And Cube Root



Important formulae and tricks and shortcuts of Square Root And Cube Root:

In Banking, Placement and Management Exams, the Quantitaive section will often test your speed. You need to be quick with calculations if you want to crack that exam. You can use this shortcut to quickly find the square root of a number which is a perfect square. We can even find square roots of large numbers. But this method is most ideally used for four or five digit perfect squares. You can use this trick for IBPS PO, IBPS Clerk, SBI Clerk, SBI PO and SBI Associate exams and all other competative exams.

(Unit) Single Digits of Squares:

First we need to remember unit digits of all squares from 1 to 10. The figure below shows the unit digits of the squares.


Now from above diagram can say that, whenever the unit digit of a number is 9, unit digit of the square root of that number will be definitely 3 or 7. Similarly, this can be applied to other numbers with different unit digits.

Find Square Root of a Four Digit Number:

Let’s learn how to find square root by taking different examples.

Example: Find the square root of 4489.

We group the last pair of digits, and the rest of the digits together.

Now, since the unit digit of 4489 is 9. So we can say that unit digit of its square root will be either 3 or 7.


Now consider first two digits i.e. 44. Since 44 comes in between the squares of 6 and 7 (i.e. 62 < 44 < 72), so we can definitely say that the ten’s digit of the square root of 4489 will be 6.  So far, we can say that the square root will be either 63 or 67.

Now we will find the exact unit digit.

To find the exact unit digit, we consider the ten’s digit i.e. 6 and the next term i.e. 7.

Multiply these two terms


Since, 44 is greater than 42. So square root of 4489 will be the bigger of the two options i.e. 67.
Let us take another example.

Example: What is the square root of 7056?


Unit digit will be 4 or 6.

Since, 82 < 70 < 92

So the square root will be either 84 or 86.

Now consider 8 and 9



Since, 70 is less than 72. So square root will be the lesser of the two values i.e. 84.

Let’s try it out with five digit numbers now!

Find Square Root of a Five Digit Number:

We pair the digits up starting from the right side. Since there is one extra left over after two pairs are formed, we club it with the pair closest to it.

Example: √(16641) = ?


Unit digit will be 1 or 9.

Since, 122 < 166 < 132

So, the square root will definitely be 121 or 129.

Now, consider 12 and 13


Since, 166 is greater the 156, we pick the larger of the options i.e. 129.


Let’s take another example, so that this trick will be clear to you.

Example: √(33489) = ?


Unit digit will be 3 or 7.

Since, 182 < 334 < 192

So, square root will be 183 or 187.

Now consider 18 and 19.


Now, 334 is less than 342. So, the square root will be lesser of the two numbers i.e. 183.


Shortcut to find the cube root of any 5 or 6 digit number:

Step 1:Find the cube root of the last digit.
Points to be remembered while using this method.
(1)If the last digit is 8 then cube root will be 2.
(2)If the last digit is 2 then cube root will be 8.
(3)If the last digit is 7 then cube root will be 3.
(4)If the last digit is 3 then cube root will be 7.
(5)If the last digit is any other digit other than 2,8,3,7 then put the same number.
From this step you will get the unit’s or one’s place digit.


To find the tenth place digit you need to follow the below steps.

Step 2:Strike out the last 3 digits of the given number.


Step 3: find the nearest cube of the remaining number.

Step 4: find the cube root of the nearest cube which will give you ten’s place digit.

For solved problems on above formulas please visit below sections: