Square Root 1 to 50
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Last updated on August 5, 2025

The square root of any number is the value that, when the value is multiplied by itself twice you get the given number again. It is used for measuring diagonals in mathematics, finding kinetic energy and velocity in physics, etc. In this topic, we shall learn more about square root from 1 to 50.

Square Root 1 to 50

The square root of a number and squaring a number are the inverse or opposite operations of a number. Square of a number is a value that you get when you multiply the given number (x) by itself twice, it is called squaring a number (squared). Whereas, the square root of a number is a number value that when the value (y) multiplied by itself twice, gets the original given number (x).

For example, if you are given a number x, the square of that number is x × x = x2. And the square root of that number is, √x = y, where when you multiply y twice, you get x. 

Square Root 1 to 50 Chart

This square root chart from 1 to 50 will be a great help for kids who are struggling with finding square roots by approximation.

This is a helpful tool because it shows the square roots of both perfect squares like 1, 4, 9, 16, etc.

And the approximate square roots of numbers that are not perfect squares like 2, 3, 5, etc. 
 

List of Square Root 1 to 50

Provided below are the square roots from 1 to 50 in five different charts and how they are used in different fields.

Here is a list of all the square roots from 1 to 50:

Square Root from 1 to 10

     Square roots from 1 to 10 are fundamental in mathematics, helping us solve daily life equations and understand geometric concepts. They are especially useful in areas like algebra, geometry, and basic physics.

Square Root from 11 to 20

Square roots from 11 to 20 are useful in various calculations, particularly in algebra and geometry. They help simplify expressions and are often used in real-world applications like measurements and construction.

Square Root 21 to 30

Square roots from 21 to 30 are essential in solving equations and understanding geometric properties. These are frequently used in fields such as engineering, physics, and architecture.
Square Root 31 to 40

Square roots from 31 to 40 play a crucial role in mathematical computations and real-world problem-solving. They are often applied in areas like physics, engineering, and data analysis.

Square Root 41 to 50

Square root from 41 to 50 is valuable in various mathematical and scientific contexts. These roots help simplify complex equations and are used in fields such as physics, statistics, and engineering.

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Square Root 1 to 50 for Perfect Squares

A square root chart for perfect squares from 1 to 50 lists the square roots of integers that are perfect squares within this range.

For example, perfect squares like 1, 4, 9, 16, 25, 36, and 49 will have square roots 1, 2, 3, 4, 5, 6, and 7, respectively, displayed in the chart. 
 

Square Root 1 to 50 for Non-perfect Squares


A square root chart for non-perfect squares from 1 to 50 shows approximate values of square roots for integers that are not perfect squares within this range.

These values are usually rounded to one or more decimal places since they are irrational numbers, such as √2 ≈ 1.41 or √7 ≈ 2.65.

How to Calculate Square Roots 1 to 50

There are several ways to calculate the square root of numbers from 1 to 50, be it for quick estimation or precise answers.

Here are two of the easiest methods to find the square root of any given number.
 

Prime Factorization Method

Prime factorization is a way to represent a given number as a product of its prime numbers.

In order to find the square root of a given number through prime factorization, we need to follow these given steps:

Step 1: Let’s consider the given number as 36, for example.

Step 2: Now, perform the prime factorization of 36.

    Start dividing 36 by the smallest prime number 2

        36 ÷ 2 = 18

    Divide 18 by 2 again

             18 ÷ 2 = 9

    Divide 9 by 2 

        9 ÷ 2 = 4 (quotient) and 1 (remainder)

    Since 9 isn’t divisible by 2, we take the next prime number and continue dividing

        9 ÷ 3 = 3

    Divide 3 by 3 again

        3 ÷ 3 = 0

    Thus, we can say that the prime factorization of 36 is 

        36 = 2 × 2 × 3 × 3 = 22 × 32

Step 3: Group the prime factors in pairs

        22 × 32 = (2 × 2) (3 × 3)

Step 4: Take one number from each pair 

        (2 × 2) ⇒ 2

        (3  3) ⇒ 3

Step 5: Multiply the two numbers

        2 × 3 = 6

Thus, the square root of 36 is 6.
 

Division Method

In the division method, large numbers are broken down into smaller simpler steps, breaking the division problem into a chain of easier steps.

Let’s understand the steps one by one:

Step 1: First, pair the digits of the number (starting from the unit's place).

 Since 36 has only two digits, it forms one group = 36

Step 2: Find the largest number whose square is less than or equal to the given number.

 The largest number whose square is ≤ 36

 6 × 6 = 36, so 6 is the largest number 

  Write 6 as the first digit of the square root.

Step 3: Subtract the square of 6 from the number 36.

Subtract 62 = 36 from 36

36 – 36 = 0

Since the remainder is 0, the division process ends here.

Thus, the square root of 36 is 6.
 

Rules for Calculating Square Root 1 to 50

Rule 1: Simplify square roots for perfect squares.

Rule 2: Approximation for non-perfect squares.

Rule 3: Use of fractions for roots of decimals.

Rule 4: Avoid making errors while rounding a number.
 

Tips and Tricks for Square Root 1 to 50

  • The simplest and easiest trick to find a square root is to memorize the perfect squares, that is from 12 to 102. This will help the kids find the squares of numbers between 1 to 100.
     
  • Try drawing a grid on a piece of paper where you square numbers and color in squares to represent the perfect squares. This can help you visualize how square roots work.
     
  • Always break down steps into simple steps in order to find the square root faster.
     

Common Mistakes and How to Avoid Them in Square Roots 1 to 100

Download Worksheets

Problem 1

Find the square root of 49 using prime factorization.

Okay, lets begin

√49 = 7

Explanation

Prime factorization of 49 = 7 × 7

Group the factors: (7 × 7)

Take one number from the group = 7

Thus, the square root of 49 is 7

Well explained 👍

Problem 2

Estimate the square root of 20 to one decimal place.

Okay, lets begin

√20 ≈ 4.5

Explanation

Identify the perfect squares around 20

 16 = 42 and 25 = 52

  √20 lies between 4 and 5

    Using approximation, that is try multiplying 4.1, 4.2, 4.3,...

            4.1 × 4.1 = 16.81

            4.2 × 4.2 = 17.64

            4.3 × 4.3 = 18.49

            4.4 × 4.4 = 19.36

            4.5 × 4.5 = 20.25

    So we can conclude that √20 lies between 4.4 and 4.5.

    When approximating it into one decimal place, you get √20 ≈ 4.5.

Well explained 👍

Problem 3

Find the square root of 16/25

Okay, lets begin

 16/25 = 0.8
 

Explanation

Take the square root of the numerator and denominator separately

  16/25 = 4/5 = 0.8
 

Well explained 👍

Problem 4

Which number between 1 and 50 has a square root of approximately 7?

Okay, lets begin

The number is 49.

Explanation

First, let’s find the square root of numbers between 1 and 50 that are close to 7.

The number 36 is a perfect square, which is 6 × 6 = 36

Now we know that 36 is a perfect square, and it is near to 49. 

Try with the next number 7. 

When you multiply 7 × 7, you get 49. 

Thus, the number 49 is the approximate square root of 7

Well explained 👍

Problem 5

What is the square root of 1 and how is it different from other square roots?

Okay, lets begin

The square root of 1 is 1.

Explanation

The square root of 1 is the number that when we multiply by itself equals 1.

That is, 1 × 1 = 1, so the square root of 1 is also 1.

Unlike the other numbers, 1 is the only number whose square root is itself. 

Well explained 👍

FAQs on Square Root 1 to 50

1.What are the perfect squares between 1 and 50?

The perfect squares are 1, 4, 9, 16, 25, 36, and 49.
 

2.Why are some square roots irrational?

If a square root cannot be represented as a fraction of two integers. That is p/q, where q ≠ 0, it is an irrational number. When the integer is not a perfect square, something occurs.

3.How do you estimate the square root of non-perfect squares?

To estimate, find the two closest perfect squares the number lies between and then find the value through the approximation method. For example, for 18, it lies between 16 (42) and 25 (52), so its square root is slightly more than 4.

4.What is the square root of 25?

The square root of 25 is 5.
 

5.Can square roots be negative?

Mathematically, square roots can be positive or negative because both x2 and (-x2) equal x2. However, the principal square root (used commonly) is positive.
 

Important Glossaries for Square Root 1 to 50

  • Square Root: Square root of a number is a value (y) that, when the value is multiplied by itself, equals the original given number (x). For example, the square root of 16 is 4 because 4  4 = 16.
  • Perfect Squares: Perfect squares are numbers that are the product (sum) of integers multiplied by itself. For example, 1, 4, 9, 16, 25 are perfect squares because they result from 12, 22, 32, 42, 52 respectively. 
  • Prime Factorization: The process of expressing a number as the product of its prime numbers (prime factors). For example, the prime factorization of 36 is 2 × 2 × 3 × 3 = 22 × 32.

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