Class 8 Maths Square and Square Roots NCERT Concepts- PlanetSpark

Have you ever wondered how to quickly calculate the area of a square field or estimate numbers without a calculator? That’s exactly where squares and square roots come into play. These concepts are not just important for exams and they help you build strong problem-solving skills for real-life situations too.

In Class 8 Maths, the chapter on Squares and Square Roots is a foundational topic in NCERT. It introduces you to patterns, shortcuts, and logical thinking that make maths simpler and even fun! In this blog, we’ll break down every concept in an easy, conversational way so you can understand, practice, and master it confidently.

What Are Squares?

A square of a number means multiplying the number by itself.

Formula:
Square = Number × Number

Examples:
2² = 4
5² = 25
12² = 144

This concept is simple but very powerful. It forms the base for understanding square roots and many algebraic expressions later on.

Understanding Perfect Squares

A perfect square is a number that is the square of a whole number.

Examples:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100

These numbers have exact square roots.

Key idea:
If a number has a whole number as its square root, it is a perfect square.

Important Properties of Square Numbers

1. Unit Digit Pattern

Square numbers can only end in certain digits.

Possible last digits: 0, 1, 4, 5, 6, 9

Numbers ending in 2, 3, 7, or 8 can never be perfect squares.

2. Even and Odd Squares

Square of an even number is always even.
Square of an odd number is always odd.

Example:
6² = 36 (even)
7² = 49 (odd)

3. Pattern in Differences

The difference between consecutive square numbers follows a pattern:

2² − 1² = 3
3² − 2² = 5
4² − 3² = 7

This pattern continues with odd numbers.

4. Number of Zeros in Square

If a number ends with zeros, its square will have even number of zeros.

Example:
10² = 100
100² = 10000

Methods to Find Squares Easily

1. Direct Multiplication

Example:
14² = 14 × 14 = 196

2. Using Identity

(a + b)² = a² + 2ab + b²

Example:
(20 + 3)² = 20² + 2×20×3 + 3²
= 400 + 120 + 9 = 529

3. Square of Numbers Ending in 5

Shortcut:
n5² = n × (n + 1) followed by 25

Example:
35² = 3 × 4 = 12 → 1225
85² = 8 × 9 = 72 → 7225

Help your child master squares and square roots with expert guidance and interactive learning. 

Book a free trial today.

What Are Square Roots?

A square root is the reverse of squaring a number. It tells you which number was multiplied by itself to get the given number.

Symbol: √

Examples:
√9 = 3
√64 = 8
√100 = 10

Methods to Find Square Roots

1. Prime Factorization Method

Steps:

1. Break the number into prime factors

2. Make pairs of the same numbers

3. Take one number from each pair

Example:
Find √144

144 = 2 × 2 × 2 × 2 × 3 × 3
Pairs: (2,2), (2,2), (3,3)
Square root = 2 × 2 × 3 = 12

2. Long Division Method

This method is useful for large numbers.

Example:
√2025 = 45

This method may look lengthy at first, but with practice, it becomes easy and accurate.

3. Estimation Method

Used when the number is not a perfect square.

Example:
Find √50

Closest squares are:
49 (7²) and 64 (8²)

So, √50 is slightly more than 7.

Make Maths Simple and Fun
Turn confusion into confidence with engaging sessions designed for Class 8 students. Book a free trial now.

Perfect Squares to Remember

Memorizing squares helps in faster calculations.

1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100

Students should try to remember squares at least up to 20 or 30.

Applications of Squares and Square Roots

1. Area Calculation

Area of a square = side × side

If the side is 8 cm, area = 64 cm²

2. Finding Length

If the area is given, you can find the side using square roots.

Example:
Area = 121 cm²
Side = √121 = 11 cm

3. Real-Life Use

Used in construction, measurement, and design.
Also used in advanced topics like algebra and geometry.

Common Mistakes to Avoid

Students often make simple errors in this chapter.

• Confusing square and square root

• Forgetting to pair numbers in prime factorization

• Making calculation errors

• Not recognizing perfect squares

Avoiding these mistakes can improve accuracy significantly.

Improve Speed and Accuracy in Exams
Give your child the skills to solve maths problems faster and correctly. Book a free trial class today.

NCERT Practice Questions

1. Find the squares:

a) 16
b) 21
c) 35

2. Find the square roots:

a) 169
b) 256
c) 441

3. Check if the following are perfect squares:

a) 800
b) 900
c) 1225

4. Problem Solving

Find the smallest number by which 75 must be multiplied to make it a perfect square.

Why Squares and Square Roots Are Important in Class 8

Squares and square roots are more than just another chapter in your Class 8 maths syllabus—they form the base for many advanced topics you will study later. Concepts like algebra, geometry, and even higher-level calculations rely heavily on your understanding of these fundamentals. When students clearly understand how numbers behave when squared or square-rooted, they develop stronger logical thinking skills.

This chapter also improves mental maths abilities. For example, if you know squares up to 20, you can solve many problems quickly without writing long calculations. It also helps in competitive exams where speed matters. Beyond academics, these concepts are used in real-life situations like calculating area, estimating values, and solving measurement problems. So, mastering this chapter early gives you a long-term advantage in maths.

Easy Strategies to Practice and Remember Squares

One of the biggest challenges students face is remembering square numbers. However, with the right strategies, this becomes much easier. Instead of memorizing randomly, focus on patterns. For instance, observe how the unit digits of square numbers repeat in a certain way. This helps you identify whether a number can be a perfect square or not.

Another effective method is breaking numbers into smaller parts. For example, instead of calculating 19² directly, you can use the identity (20 − 1)². This reduces effort and improves accuracy. Writing square tables daily, even for five minutes, can make a big difference over time. You can also test yourself or practice with quizzes to strengthen your memory.

Consistency matters more than long study hours. Practicing a few problems every day will help you gain confidence and reduce mistakes. Over time, you will notice that calculations become faster and more natural.

How to Approach Square Root Problems with Confidence

Square roots may seem tricky at first, especially when dealing with large numbers. However, once you understand the methods clearly, they become much easier to handle. The key is to choose the right method based on the question. For smaller numbers, prime factorization works best because it is simple and systematic. For larger numbers, the long division method is more accurate.

Another helpful approach is estimation. If you are unsure about the exact square root, try finding the nearest perfect squares. This gives you a rough idea and helps you avoid mistakes. For example, if you need to find √50, knowing that 49 and 64 are nearby squares helps you estimate quickly.

Practice is the most important factor here. The more problems you solve, the more comfortable you become with the steps. Always write each step clearly to avoid confusion. Over time, what once seemed difficult will start feeling easy and manageable.

Tips to Master Squares and Square Roots

Practice regularly instead of memorizing everything at once.
Focus on understanding patterns.
Use shortcuts where possible.
Revise square tables daily.

Consistency is the key to mastering maths.

Common Problem Areas in Squares and Square Roots

Many Class 8 students find this chapter confusing at first. The biggest issue is not the difficulty of the topic, but the lack of conceptual clarity. Students often try to memorize squares instead of understanding patterns. This leads to errors during exams. Another common problem is mixing up squares and square roots, which creates confusion in solving questions. Building a strong base and practicing regularly can help overcome these challenges.

Mistakes Students Make While Solving Questions

One of the most common mistakes is incorrect prime factorization. Students either skip steps or fail to pair factors properly, which leads to wrong answers. Another issue is calculation errors while finding squares of larger numbers. 

Many students also assume that any number close to a perfect square is itself a perfect square, which is not true. Careless mistakes and lack of revision also affect performance in this topic.

Proven Tips to Improve Performance in Exams

To score well in exams, focus on understanding concepts instead of rote learning. Practice a mix of easy and challenging questions to build confidence. Revise square tables daily and test yourself regularly. Pay attention to step-by-step solving methods, especially in long division and factorization. Most importantly, stay calm during exams and double-check your calculations to avoid simple errors.

Why Choose PlanetSpark for Maths Learning

PlanetSpark helps students move beyond rote learning and truly understand maths concepts with clarity and confidence. The focus is on making topics like squares and square roots simple, engaging, and easy to apply in exams. With expert mentors and structured sessions, students build strong problem-solving skills step by step.

• Personalized learning plans based on student level

• Interactive sessions with real-life examples

• Focus on speed, accuracy, and concept clarity

• Regular practice worksheets and doubt-solving support

• Boosts confidence for school exams and beyond

Conclusion

Squares and square roots are one of the most important topics in Class 8 Maths. They build a strong foundation for higher-level maths and improve logical thinking.

By understanding the concepts, practicing regularly, and using the right methods, you can master this chapter without stress. Maths should feel like solving exciting puzzles. So, you will explore carefully explained math olympiad practice questions.