Square Root 1 to 30

Understanding the square roots from 1 to 30 is important in mathematics. Square roots are key concepts used in algebra, geometry, and solving real-world problems. This guide breaks down the square roots from 1 to 30. It includes a square roots chart, a list of square roots, and methods for calculating them. It also distinguishes between perfect square numbers and non-perfect squares in this range.  

 

Table of Contents

 

What Are Square Roots?  

The square root of a number is a value that, when multiplied by itself, gives the original number. For instance, the square root of 9 is 3 because 3 × 3 equals 9. Square roots can be perfect or non-perfect. Knowing both types helps master math operations from 1 to 30.  

 

Square Roots of Numbers Between 1 to 30   

This list of square roots offers a quick reference to square root values from 1 to 30. It includes both perfect squares and non-perfect squares.  

 

Radical Form

Approx. Square Root Value 

1

1.000

2

1.414

3

1.732

4

2.000

5

2.236

6

2.449

7

2.646

8

2.828

9

3.000

10

3.162

11

3.317

12

3.464

13

3.606

14

3.742

15

3.873

16

4.000

17

4.123

18

4.243

19

4.359

20

4.472

21

4.583

22

4.690

23

4.796

24

4.899

25

5.000

26

5.099

27

5.196

28

5.291

29

5.385

30

5.477

 

Use this individual list of square roots as a study reference or for calculation. Whether you're identifying perfect square numbers or estimating square root values, this breakdown of square root 1 to 30 will help you understand and apply these numbers accurately.

 

Perfect and Non-Perfect Squares (1 to 30)  

A perfect square is a number that is the square of an integer. In other words, when an integer is multiplied by itself, the result is a perfect square. The square root of a perfect square is always a whole number.

Square Root 1 to 30 for Perfect Squares  

Here are the square root values for perfect square numbers between 1 and 30:

  • √1 = 1

  • √4 = 2

  • √9 = 3

  • √16 = 4

  • √25 = 5

These roots are whole numbers and do not need further approximation.  

 

Square Root 1 to 30 for Non-Perfect Squares  

A non-perfect square is a number that cannot be expressed as the square of a whole number. In other words, their square root values are irrational, meaning the decimals go on without repeating. 
Here’s a list of square roots from 1 to 30 that are non-perfect squares with approximate values up to three decimal places:  

 

Number

Square Root (Approx.)

2

2≈1.414

3

3≈1.732

5

5≈2.236

6

6≈2.449

7

7≈2.646

8

8≈2.828

10

10≈3.162

11

11≈3.317

12

12≈3.464

13

13≈3.606

14

14≈3.742

15

15≈3.873

17

17≈4.123

 

18

18≈4.243

19

19≈4.359

20

20≈4.472

21

21≈4.583

22

22≈4.690

23

23≈4.796

24

24≈4.899

26

26≈5.099

27

27≈5.196

28

28≈5.291

29

29≈5.385

30

30≈5.477

 

These values in the square roots chart are approximated to three decimal places and used in daily mathematical applications. Since these are not perfect square numbers, you can’t simplify them to whole numbers.

 

How to Calculate Square Roots from 1 to 30?  

Square roots are numbers that, when multiplied by themselves, give the original number.
For example:
25=5because 5×5=25
 
There are several ways to calculate square roots. Two of the most common and useful methods are prime factorization and the long division method.
 
Method 1: Prime Factorization
 
This method is used for perfect squares (numbers whose square roots are whole numbers).
 
Steps:
  1. Break the number into its prime factors.
  2. Make pairs of the same prime factors.
  3. Take one number from each pair and multiply them.
 
Example 1: Find 36
 
36=2×2×3×3
 
 
Now, make pairs:
 
36=(2×2)×(3×3)
 
 
 
Take one number from each pair:
 
36=2×3=6
 
So, the square root of 36 is 6.
 
 
Example 2: Find 49
 
49=7×7
49=7
 
This method only works easily with perfect squares like 1, 4, 9, 16, 25, 36, 49, etc.
 
Method 2: Long Division Method
 
This method is used for non-perfect squares where the answer is not a whole number. It gives a more precise value, including decimals.
 
Steps :
  1. Pair the digits of the number from right to left.
  2. Find the largest number whose square is less than or equal to the first group.
  3. Subtract and bring down the next pair of digits.
  4. Double the divisor, add a digit, and continue dividing.
  5. Repeat to get the value correct up to the required decimal places.
 
Example: Find 20
 
Using the long division method:
 
20 lies between 16=42 and  25=52
 
So, the answer will be between 4 and 5.
 
Applying long division, we get:
 
20​≈4.472
 
This gives an accurate decimal value for non-perfect squares.

 

Square Root Values in Radical and Exponential Forms  

Each square root from 1 to 30 can be shown in both radical and exponential forms:  

Square Root in Radical Form

  • The symbol is called the radical sign.

  • Writing a means “the square root of a”.

Examples:

  • 25=5

  • 4=2

  • 2≈1.414(This is an irrational number because its value cannot be expressed exactly, only approximately as 1.414…)

Radical form is simple and often used in basic arithmetic.

 

Square Root in Exponential Form

In mathematics, roots can also be expressed using exponents (powers).

  • The rule is:
    a=a12

Examples:

  • 25=2512=5

  • 4=412=2

  • 2=212

Here, the exponent 1/2 means “take the square root.”

This form is very useful in algebra and higher classes because it is easier to apply the rules of exponents than radicals. Using both forms helps in understanding how to represent square root values flexibly.  

 

Solved Examples on Square Root 1 to 30

Example 1: Find the value of 25+9
 
Solution:
 
We know:
 
25=5,9=3
 
So substituting the value in the given expression, we get,
25+9=5+3=8
 
Hence, the value is 8.
 
 
Example 2: Simplify 34+21
 
Solution:
 
We know:
 
4=2,1=1
 
So substituting the value in the given expression, we get,,
 
34+21=3(2)+2(1)
   =6+2=8
 
Hence, the simplified form is 8.
 
 

Example 3: Simplify 36+9
Solution:
We know:

36=6,9=3

So substituting the value in the given expression, we get,,

36+9=6+3=9

Hence, the value is 9.

 

Example 4: Find the value of 52  (non-perfect square).

Solution:

We know:

2≈1.414

So substituting the value in the given expression, we get,,

52=5×1.414=7.07

Hence, the value of   52   is approximately 7.07.



Example 5: Which two integers does 17 lie between?

  • 17≈4.123

  • 16=4and 25=5

So, 17 lies between 4 and 5

 

Conclusion  

Understanding the square roots from 1 to 30 is basic for further math learning. This guide explained perfect square numbers, included a full square roots chart, and showed how to find square roots using prime factorization and long division. Whether you're looking for a list of square roots, learning to estimate square root values, or exploring their different forms, mastering this topic gives you an advantage in both school and real-world math.

 

Frequently Asked Questions on Square Roots

1. What is 3 of value?

Answer: The value of 3 (square root of 3) is approximately 1.732. It is an irrational number and cannot be expressed exactly as a simple fraction.

 

2. What is 2 of value?

Answer: The value of 2 (square root of 2) is approximately 1.414. Like 3, it is also an irrational number.

 

3. How to solve 3?

Answer: To solve or estimate 3 manually, you can use methods like long division, approximation, or a calculator. One way to estimate is by trying successive squares:

For example,

1.7² = 2.89

1.73² = 2.9929

1.732² ≈ 3.0001 → So 3≈1.732

 

4. How to find 5 value?

Answer: The value of 5 (square root of 5) is approximately 2.236. You can find it using a calculator or by estimation methods similar to those used for 3.

 

Learn square roots from 1 to 30 the easy way with charts and tips at Orchids The International School!

 

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