Square Root From 1 To 25 Complete List and Explanation

The concept of Square Root from 1 to 25 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Knowing the square roots of numbers from 1 to 25 makes it easy to simplify equations and solve problems faster, especially for students preparing for exams like CBSE, NTSE, and Olympiads.

What Is Square Root from 1 to 25?

A square root of a number is a value that, when multiplied by itself, gives that number. For example, the square root of 16 is 4 because 4 × 4 = 16. The symbol for square root is √. Square Root from 1 to 25 means you find the square roots of all natural numbers between 1 and 25. In maths, this concept is seen in geometry, algebra, and real-life measurements.

Key Formula for Square Root

Here’s the standard formula: \( \sqrt{x} \times \sqrt{x} = x \ )
For example: \( \sqrt{9} \times \sqrt{9} = 9 \).

Square Root Table from 1 to 25

Number	Square	Square Root (√ )
1	1	1.000
2	4	1.414
3	9	1.732
4	16	2.000
5	25	2.236
6	36	2.449
7	49	2.646
8	64	2.828
9	81	3.000
10	100	3.162
11	121	3.317
12	144	3.464
13	169	3.606
14	196	3.742
15	225	3.873
16	256	4.000
17	289	4.123
18	324	4.243
19	361	4.359
20	400	4.472
21	441	4.583
22	484	4.690
23	529	4.796
24	576	4.899
25	625	5.000

Cross-Disciplinary Usage

Square Root from 1 to 25 is not only used in maths but also in physics (for calculating distances and areas), in computer science (algorithms and search), and even in logical reasoning questions. JEE and NEET often include MCQs where knowing these roots saves valuable time.

Perfect Squares from 1 to 25

The numbers 1, 4, 9, 16, and 25 are called perfect squares, because their square roots are whole numbers (1, 2, 3, 4, and 5). These are easy to memorize and appear often in exams.

How to Find Square Root Manually

You can find the square root of a number using two main methods: Prime Factorization and Long Division.

Method 1: Prime Factorization

Example: Find the square root of 144

1. Write 144 as product of its prime factors

144 = 2 × 2 × 2 × 2 × 3 × 3

2. Make pairs: (2 × 2), (2 × 2), (3 × 3)

3. Take one number from each pair: 2 × 2 × 3 = 12

So, √144 = 12

Method 2: Long Division

Use this for non-perfect squares:

1. Group the number in pairs from right

2. Find the largest square number less than your group, subtract, and bring down the next group

3. Repeat until you get the desired decimal places

Solved Example

Example: Find the value of √18

1. 18 does not have an exact square root since it is not a perfect square.

2. By estimation, it lies between √16 and √25 (which are 4 and 5).

3. Use a calculator or the long division method to get √18 ≈ 4.243.

Speed Trick to Memorise Square Roots 1 to 25

Here’s a simple pattern: Square roots of perfect squares (like 1, 4, 9, 16, 25) are whole numbers. Roots of numbers in between (like 2, 3, 5, 6, etc.) are decimals, so just remember the nearest perfect squares to estimate quickly in exams.

Tip: Remember that for any number x, if x is between 16 and 25, then √x will be between 4 and 5.

Try These Yourself

• What is the square root of 49?
• Estimate √23 using the table above.
• Is 13 a perfect square?
• Find the square of 7 and then find its square root.
• Write the value of √1/25 as a fraction.

Frequent Errors and Misunderstandings

• Confusing square roots with squares (e.g., thinking √16 = 8 instead of 4).
• Forgetting only positive roots are natural (negative roots are not natural numbers).
• Misplacing decimals and making calculation errors in exams.

Where is Square Root from 1 to 25 Used?

You’ll use Square Root from 1 to 25 when calculating areas, working with quadratic equations, or finding solutions to word problems. In geometry, it helps find length of square sides from given area. In Pythagoras theorem or quadratic equations, square roots show up regularly.

Relation to Other Concepts

Learning Square Root from 1 to 25 also links closely with the topics Square Root Table, Perfect Squares, and Squares and Square Roots. Mastering these will support future chapters and help you score well in competitive exams.

Classroom Tip

A quick way to remember: Perfect squares have whole number roots (like 1, 4, 9, 16, 25). For the numbers in between, round to the closest perfect square to estimate. Vedantu’s teachers use these memory-based tricks to get you ready for rapid-fire questions and MCQs.

For an extended list, check the Square Root Table and for tricky calculation methods, try the Square Root Finder tool or explore the Prime Factorization method for more practice.

We explored Square Root from 1 to 25—from definition, tricks, table, and solved examples, to where you’ll use it in real problems. Try regular practice and use Vedantu’s study resources to become confident at handling square roots in all maths classes.