Rationalizing the Denominator | Class 9 Maths | CBSE & ICSE | 4 Solved Examples Explained

📚 Rationalizing the Denominator | Class 9 Maths | CBSE & ICSE Boards | 4 Solved Examples
🎓 By: Learn Smart with Sweta

Welcome to Learn Smart with Sweta – your one-stop destination for understanding Maths and Science concepts in a simple, clear, and engaging way!
In this video, I explain one of the most important concepts from the Number System chapter of Class 9 Mathematics – Rationalizing the Denominator.

This topic is crucial for students of both CBSE and ICSE Boards, as it forms a strong foundation for higher classes and is frequently asked in exams.

📌 What is Covered in This Video?
In this session, I have focused only on Rationalizing the Denominator, which is a part of the larger chapter on Rational and Irrational Numbers.

🔍 The following key points are explained:

✅ What does it mean to rationalize the denominator?

✅ Why do we rationalize the denominator?

✅ Step-by-step method to rationalize different types of irrational denominators.

✅ Concept of conjugates and their role in rationalization.

✅ Four carefully chosen and fully solved examples to cover a variety of problems.

📘 Examples Solved in the Video:
Simple Rationalization
Example:
1
3
3
​

1
​
→ Multiply numerator and denominator by
3
3
​


Rationalizing with Binomial Surds
Example:
1
3
+
2
3
​

2
​

1
​
→ Use conjugate
3
−
2
3
​
−
2
​


Numerical Rationalization Involving Multiples
Example:
5
2
5
2
5
​

5
​
→ Multiply with
5
/
5
5
​
/
5
​


Advanced Level Question for Better Understanding
Example:
3
+
2
5
−
2
5−
2
​

3+
2
​

​
→ Multiply by conjugate
5
+
2
5+
2
​


These examples are explained in a slow and clear manner with step-by-step calculations, so that students can follow along and practice simultaneously.

📘 What is Rationalizing the Denominator?
Rationalizing the denominator means converting a fraction with an irrational number in the denominator into an equivalent fraction where the denominator is a rational number.

For example,
1
2
⇒
1
×
2
2
×
2
=
2
2
2
​

1
​
⇒
2
​
×
2
​

1×
2
​

​
=
2
2
​

​

Now the denominator is rational!

This is particularly useful in simplifying expressions and is a common skill required in algebraic manipulation in higher classes.

🏫 Who Should Watch This Video?
✅ Class 9 Students from CBSE and ICSE Boards
✅ Students preparing for school exams, unit tests, and Olympiads
✅ Anyone who wants a clear and conceptual understanding of rationalizing denominators
✅ Teachers and tutors looking for a simple way to explain this concept to their students

📈 Why is this Topic Important?
Rationalizing the denominator:

Helps in simplifying expressions

Is a frequently asked question type in exams

Is a stepping stone for algebraic expressions, surds, and quadratic equations in higher grades

Develops algebraic manipulation skills

🧠 Learning Outcomes from this Video:
After watching this video, you will be able to:
✔ Understand the logic behind rationalizing denominators
✔ Apply the concept of conjugates correctly
✔ Solve problems involving irrational numbers in the denominator
✔ Tackle exam questions with confidence

💡 Tips While Watching the Video:
📌 Keep a notebook and pen ready
📌 Pause and try each example yourself
📌 Note down important steps and tips
📌 Comment below if you have any doubts or want more examples

🔔 Don’t Forget to:
👍 Like the video if you found it helpful
📝 Comment your feedback and doubts
📤 Share this video with your classmates and friends
✅ Subscribe to Learn Smart with Sweta for more such conceptual videos
🔔 Press the bell icon to get notified when new videos are uploaded

🔗 Related Videos You May Like:
🎥 Shares and Dividends – ICSE Class 10
🎥 Arithmetic Progression (AP) – CBSE & ICSE Class 10
🎥 Introduction to Algebraic Identities
🎥 How to Simplify Surds Step-by-Step

📬 Stay Connected:
Follow this channel for regular updates and upcoming videos on:

CBSE & ICSE Mathematics (Classes 6–10)

Science Concepts Explained with Visuals

Board Exam Preparation Tips

Practice Questions and Test Series

Thank you for watching and learning with Learn Smart with Sweta!
Let’s make learning simple, smart, and fun 😊