how to get rid of square root

How To Find Square Root of a Number – Learn Square Root Tricks Here!

Naveen | Updated: May 20, 2020 19:00 IST

This post is also available in: Hindi

In most of the Government Exams, whether it is the state or central government exam, Quantitative Aptitude or Numerical Ability plays a crucial role in your selection whether it is banking or SSC exams. The major thing which is essential for acing this section is speed and accuracy. The candidate who masters in these two things can score better in Quant or Numerical Ability. Often students are not aware of the shortcuts being used to solve the problem and eventually find themselves trapped during the examination. One needs to ensure that they are quick with calculations so that they stand apart from their competitors. One such trick that will help you solve many numerical problems is finding the square root. As in these examinations often calculation based questions are asked. Here in this article, you will know how to find the square root of a number. Learn the square root trick which is most ideally used for four or five-digit perfect squares. Practice these tricks and ace in the exam you are appearing for.

Download Shortcut Tricks to Find Square Root as PDF

Square Root Tricks – Unit Digits of Squares
How to Find Square Root of a Four-Digit Number – Shortcut Method?
How to Find Square Root of a Five Digit Number – Shortcut Method

Square Root Tricks – Unit 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.

Find Square Root - Testbook

As it is clear from the above image that whenever the unit digit of a number is 9, the 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.

How to Find Square Root of a Four-Digit Number – Shortcut Method?

Let's learn square root shortcuts 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 the unit digit of its square root will be either 3 or 7.

Find Square Root - Testbook

Now consider the 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 let's proceed to 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?

Find Square Root - Testbook

The unit digit will be 4 or 6.
Since, 8² < 70 < 9²
So the square root will be either 84 or 86.

Now we will 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!

How to Find Square Root of a Five Digit Number – Shortcut Method

This will be easy for you as you have practiced the square root of a four-digit number. We will 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) =?

Find Square Root - Testbook

The unit digit will be 1 or 9.
Since, 12² < 166 < 13²
So, the square root will definitely be 121 or 129.

Now, consider for 12 and 13

Since 166 is greater than 156
We pick the larger of the options i.e. 129.

Let's take another example so that this square root trick will be clear to you.

Example: √(33489) = ?

The unit digit will be 3 or 7.
Since, 18² < 334 < 19²
So, the square root will be 183 or 187.

Now we will consider 18 and 19.

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

These square root shortcuts to find the square root of a number will surely help you in your exams. Now that you have learned the basics, take different examples, and practice some more. Regular practice of these easy tricks will help you grasp good marks in the Quant or Numerical Aptitude section. You can also use the Testbook App to boost your preparations for the upcoming government examinations with the video lessons, live tests, and quizzes. And, also use the Testbook offer to get lots of various benefits and discounts to further boost your exam preparation.

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