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Square Root Table

Last updated date: 23rd May 2024
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Root Table

A table of square roots is a tabular form that shows all the natural numbers from 1 to 100, each approximating to 3 places of decimal. By taking into use this table of square roots, we are able to find the square roots of numbers, less than 100. You can use this table to identify both the squares and square roots of numbers from 1 to 100. Find below the square root table 1 to 50 for your better understanding.

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Uses and Application of Root Table Math

  • We can use the table of square roots for the purpose of estimating the squares and square roots of natural numbers from 1 to 100 as well as square roots of larger numbers.

  • We can also use square root tables to identify the approximate value of square roots. 

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Importance of Application of Root Table

We apply a long division method in order to find approximate values of square roots. The method is not only lengthy but quite difficult too. Thus, for the reason, tables of square roots and cube roots have been prepared that register these approximate values of square roots for different numbers.

How to Use Square Root Tables?

Let's take a look at how we use these square root tables. Seeing that we will be obtaining approximately values only, we use the symbol ~ to signalize the same. Values of square roots from the natural number 1 to 99 are provided in the given table up to 3 places of decimal.

A square root of a number ‘m’ is a number x such that x2= m. This is to say, a number x whose square (the outcome of multiplying the number by itself, or x × x) is ‘m’. For example,

Square of 5 i.e. 52 = 25

Square root of 5, √5 = 2.2361

Example of Finding The Square Root

For example, if we want to find the square root of 3500, we would need to look in the middle column of the square root chart until we find the number that is closest to 3500. The number in the middle column that is closest to 3500 is 3464.

Now take a look in at the number to the left of 3464 in order to find its square root. The square root of 3464 is 58.85

Thus, the approximate square root of 3500 is 58.85.

To obtain a more exact number, you can also use a calculator.

Square Roots of Negative Numbers

An ideal way to get square roots of negative numbers is to introduce a completely new form of numbers. Additionally, since we call the sets of integers and decimal numbers as real numbers, we can also strategically launch a new set of imaginary numbers to do something else wholly.

Solved Examples on Square Root

Example1: Evaluate the Square Root of the Number 1764 Using Prime Factorization


Resolve the given number i.e. 1764 into prime factors

While calculating the square root of 1764 using the prime factorization method, we get

2 x 2 x 3 x 3 x 7 x 7 = 1764

Now making the pairs of the similar factors, we get

√1764 = √ [2 x 2] x [3 x 3] x [7 x 7]

= 2 x 3 x 7

= 42

Therefore, √1764 = 42

Example 2: Find Out Square Root √5329 Using Long-Division Method.

Solution 2: First we would need to mark periods and apply the long-division method,

7) 53 29 (73


143)143 ( 429



Thus, √5329 =73

FAQs on Square Root Table

1. How Can We Find the Square Root of a Perfect Square Using a Prime Factorization Method?

In order to find the square root of a perfect square when a given number is a perfect square by applying the method of the prime factorization, we need to follow the given steps in an orderly manner:

Solve the given number into prime factors

Next, form pairs of similar factors.

Now, take the product of prime factors by selecting one factor out of every pair and you will get the perfect square.

2. How Can We Find the Square Root of Very Large Numbers?

We can easily evaluate the square root of large numbers taking into account the long division method. It becomes too easy to find the square root of a perfect square when we apply the long division method given that the numbers are very large since the technique of evaluating their square roots by factorization method becomes complex and time consuming.

3. Where Can I Find the Complete Details and List of Square Root Chart?

Whether you're looking for a complete table of square roots from 1 to 100, or a catalogue of perfect square roots or a square root chart in PDF file format, you will have your radicals covered from Vedantu! The online portal has made available the printable free PDF form of square root charts in both black and white color versions.

4. What Makes for a Perfect Square Root?

A perfect square is when we multiply any positive integer by itself. The product of that multiplication is an integer. Moreover, the square root of that value will be the original number which has also been an integer. These whole integer roots are called perfect square roots.