102 LearnersLast updated on June 9th, 2025
Square Root of 1 to 30
The square root of 1 to 30 consists of the list of all square roots from 1 to 30. Square root has both positive and negative factors. Square roots are used in construction, finance, etc. In this topic, we will learn about the techniques to learn the square root easily.
Square Root of 1 to 30
The number, when multiplied by itself, gives the original number and is called the square root of the number. For example, the square root of 16 is ±4, because multiplying 4 with itself gives 16, 4 × 4 = 16. It is the opposite of squaring a number. Square roots can be rational like √4 = 2 or irrational like √2 = 1.414.
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Square Root of 1 to 30 Chart
The square root of 1 to 30 chart helps students learn quickly the square root values. Learning square roots helps in consuming time for long equations. Given below is the square root chart from 1 to 30.
| √1 = 1 | √11 = 3.3166 | √21 = 4.5825 |
| √2 = 1.4142 | √12 = 3.4641 | √22 = 4.6904 |
| √3 = 1.732 | √13 = 3.6055 | √23 = 4.7958 |
| √4 = 2 | √14 = 3.7416 | √24 = 4.8989 |
| √5 = 2.236 | √15 = 3.8729 | √25 = 5 |
| √6 = 2.4494 | √16 = 4 | √26 = 5.099 |
| √7 = 2.6457 | √17 = 4.1231 | √27 = 5.1961 |
| √8 = 2.8284 | √18 = 4.2426 | √28 = 5.2915 |
| √9 = 3 | √19 = 4.3588 | √29 = 5.3851 |
| √10 = 3.1622 | √20 = 4.4721 | √30 = 5.4772 |
List of Square Root 1 to 30
The list of square roots from 1 to 30 can help students to understand and learn the square root easily.
Square Roots From 1 to 10
The following lists display the square root of the numbers from 1 to 10.
| √1 = 1 |
| √2 = 1.4142 |
| √3 = 1.732 |
| √4 = 2 |
| √5 = 2.236 |
| √6 = 2.4494 |
| √7 = 2.6457 |
| √8 = 2.8284 |
| √9 = 3 |
| √10 = 3.1622 |
Square Root from 11 to 20
Using the following list, kids can learn the square root of 11 to 20.
| √11 = 3.3166 |
| √12 = 3.4641 |
| √13 = 3.6055 |
| √14 = 3.7416 |
| √15 = 3.8729 |
| √16 = 4 |
| √17 = 4.1231 |
| √18 = 4.2426 |
| √19 = 4.3588 |
| √20 = 4.4721 |
Square Root from 21 to 30
The list of square roots from 21 to 30 shows the square root numbers to make sure that kids learn it quickly.
| √21 = 4.5825 |
| √22 = 4.6904 |
| √23 = 4.7958 |
| √24 = 4.8989 |
| √25 = 5 |
| √26 = 5.099 |
| √27 = 5.1961 |
| √28 = 5.2915 |
| √29 = 5.3851 |
| √30 = 5.4772 |
Square Root 1 to 30 for Perfect Square
The square root of perfect squares from 1 to 30 refers to finding the exact numbers that, when multiplied by themselves, equal perfect square numbers within this range, such as 1, 4, 9, 16, and 25. Exploring these helps us understand the concept of square roots and their relation to perfect squares.
Square Root 1 to 30 for Non-Perfect Square
The square root of non-perfect squares from 1 to 30 involves finding approximate values for numbers that do not have whole numbers as their square roots, such as 2, 3, 5, and 7. This introduces the concept of irrational numbers and how square roots are calculated or estimated.
How to Calculate Square Root 1 to 30
Calculating squares can be done using methods like prime factorization, division method, or approximation for non-perfect squares.
Prime Factorization Method
Prime factorization is a method involving breaking a number into its prime factors, pairing identical factors, and then multiplying one factor from each pair to find the square root of a perfect square. Let’s understand how to find a square root using the prime factorization method:
Step 1: Let’s consider 16 as the example
Step 2: First break down the given number into its prime factors.
16 = 2 × 2 × 2 × 2
Step 3: Group the factors into pairs
16 = (2 × 2) (2 × 2)
Step 4: Take one factor from each pair
(2 × 2) ⇒ 2
(2 × 2) ⇒ 2
Step 5: Multiply the two numbers from both the pairs
2 × 2 = 4
Thus, the square root of 16 is 4
Division Method
The division method, also known as the long division method, is a step-by-step process used to find the square root of a number by dividing it into groups of digits and estimating the square root digit by digit. This method is especially useful for finding square roots of large numbers or non-perfect squares.
Step 1: First, group the digits into pairs (from the left to right)
Consider, the number that we got is 16. 16 is two digits, so we don’t have to make it into a pair.
Step 2: Find the largest number whose square is less than or equal to the first pair.
The largest number whose square is less than or equal to the first pair of digits. For 16, the square of 4 is 16, which is equal to 16.
So, the first digit of the square root is 4.
Step 3: Subtract and bring down the next pair
Now, subtract the square of the number (4 in this case) from the first pair of digits:
16 – 16 = 0
Since there are no more digits to bring down, the remainder is 0, and the process ends here.
Thus, the square root of 16 is 4.
Rules for Calculating Square Roots 1 to 30
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 rounding errors in calculations
Tips and Tricks for Square Root 1 to 30
You can achieve faster and more accurate results by following simple tips and tricks while finding the square root of any given number. Here are some of the tips and tricks that you can follow while doing square root:
- Memorize the squares of numbers from 1 to 10, which will help you quickly identify the square root of the perfect squares.
- Use approximation for non-perfect squares, because finding the exact value of the square root for a non-perfect square is hard.
- Break down the numbers into prime factors, and complex steps into a simple step-by-step process. This makes finding square roots faster and more accurate.
- Using long division for larger numbers is advisable.
Common Mistakes and How to Avoid Them in Square Root 1 to 30
Kids while learning to square and square root, might make silly mistakes because of ignorance or confusion. Here are some of the common mistakes that kids might make and how to avoid them
Mistake 1
Confusing Square Root with Division
Kids treat the square root symbol √x as dividing the number by 2. For example, assuming √16 = 16/2 = 8. Remember that the square root means finding a number that, when squared, equals the given number. √16 = 4 because 4 × 4 = 16.
Mistake 2
Forgetting Negative Square Roots
Ignoring that both positive and negative numbers can be squared to produce the same result. For example, y2 = 16 has two solutions: y = 4 and y = – 4. Always write both solutions for equations involving y2, unless the context specifies only the positive square root.
Mistake 3
Using Incorrect Approximation for Non-perfect Squares
Making a poor estimation for non-perfect squares. For example, estimating √10 ≈ 2.5 instead of ≈ 3.16. Identify the two closest perfect squares and estimate carefully between them. For √10, it’s between √9 = 3 and √16 = 4.
Mistake 4
Skipping Steps in Prime Factorization
Missing a prime factor or pairing incorrectly. For example, while finding √36, missing a factor results in an incorrect answer. Always remember to write all the prime factors, group them into pairs, and ensure every pair contributes one factor to the square root.
Mistake 5
Misapplying the Long Division Method
Errors in pairing digits, misplacing the decimal point, or incorrect subtraction steps are some common misapplications. For this, practice the long division method step by step air the digits carefully, and verify each subtraction before proceeding to the next.
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Square Root 1 to 30 Examples
Problem 1
What is the square root of 9?
The square root of 9 is 3.
Explanation
Prime factorization of 9 = 3 × 3
Group the factors into pairs and take one out of each
3 × 3 ⇒ 3
Thus, 3 is the square root of 9.
Problem 2
What is the square root of 8 using the approximation method?
The square root of 8 is approximately 2.8.
Explanation
To find the root of 8.
First, find out the nearest perfect squares of 8.
The numbers 4 (22) and the 9 (32)
So we can guess that the square root of 8 will be anywhere between 2 and 3.
Try approximating the numbers
2.1 × 2.1 = 4.41
2.2 × 2.2 = 4.84
2.3 × 2.3 = 5.29
2.4 × 2.4 = 5.76
2.5 × 2.5 = 6.25
2.6 × 2.6 = 6.76
2.7 × 2.7 = 7.29
2.8 × 2.8 = 7.84
2.9 × 2.9 = 8.41
So, we can conclude that the square root of 8 is anywhere between 2.8 and 2.9
But by approximation √8 ≈ 2.8.
Problem 3
Find the square root of 49 using the division method.
The square root of 49 is ±7.
Explanation
First pair of the digits of 49 (since it’s a two-digit number, we only have one pair ⇒ 49)
Find the largest number whose square is less than or equal to 49.
The number 7 × 7 = 49
The square root of 49 is 7.
Problem 4
Solve √x = 6
x = 36
Explanation
To solve for x, square both sides of the equation
(√x)2 = 62
By simplifying this
x = 36
Thus, the value x is 36.
Problem 5
Solve y² = 81
y = 9
Explanation
To solve y, take the square root of both sides of the equation.
(√y)2 = √81
Which simplifies to y = 9
Thus, y = 9
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FAQs on Square Root 1 to 30
1.How many perfect squares are there between 1 and 30?
2.How do I find the square root of non-perfect squares, like 20?
3.What is the square root of 1?
4.Why does the square root of a number sometimes include decimals?
5.What are some common applications of Square roots?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 1 to 30?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 1 to 30?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
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Important Glossaries for Square Roots 1 to 30
Square Root: The square root of a number is a value that, when multiplied by itself, equals the original number. For example, the square root of 16 is ±4 because 4 × 4 = 16.
Perfect Squares: A perfect square is a number that is the result of squaring a whole number. Examples include 1, 4, 9, 16, and 25.
Non-perfect Squares: A non-perfect square is a number that does not have a whole number as its square root, such as 2, 3, 5, or 7.
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