RD Sharma Class 9 Maths Rationalisation Solutions - Free PDF Download
FAQs on RD Sharma Solutions for Class 9 Maths Chapter 3 - Rationalisation
1. What is the step-by-step method to solve rationalisation problems in RD Sharma for Class 9 Maths Chapter 3?
To solve rationalisation problems from RD Sharma, you first need to identify the denominator. If the denominator is a monomial (e.g., √a), multiply the numerator and denominator by √a. If it is a binomial (e.g., a + √b), you must multiply the numerator and denominator by its conjugate (a - √b). This process uses algebraic identities to remove the surd from the denominator.
2. How do you find the values of 'a' and 'b' in complex rationalisation questions found in RD Sharma?
These are a common type of higher-order thinking skill (HOTS) question in RD Sharma. The method involves these steps:
- First, simplify the left-hand side (LHS) of the equation by rationalising the denominator completely.
- Once simplified, the LHS will be in the form of x + y√z.
- Equate this with the right-hand side (RHS), which is typically in the form a + b√z.
- By comparing the rational parts (x = a) and the irrational parts (y√z = b√z), you can determine the values of 'a' and 'b'.
3. How are the rationalisation problems in RD Sharma different from those in the NCERT textbook for Class 9?
The primary difference is in the level of difficulty and variety of questions. The NCERT textbook establishes the foundational understanding of rationalisation with simpler monomial and binomial denominators. RD Sharma, on the other hand, provides extensive practice with more complex and challenging problems, including multi-step simplifications and application-based questions, preparing students for a higher level of difficulty in exams.
4. Why is rationalising the denominator considered a necessary step for simplifying expressions with surds?
Rationalising the denominator is crucial because it converts the denominator into a rational number, which is a standard mathematical convention. This process offers two main advantages:
- It creates a standardised format, making it easier to compare or perform arithmetic operations like addition or subtraction with other fractions.
- Calculations become significantly simpler with an integer in the denominator as opposed to an irrational number, reducing the chances of errors.
5. What is the role of the algebraic identity (a+b)(a-b) = a² - b² in Chapter 3, Rationalisation?
This identity is the cornerstone of rationalising binomial denominators. When you multiply a binomial surd (like √x + √y) by its conjugate (√x - √y), you apply this identity. The result, (√x)² - (√y)² = x - y, effectively eliminates the square roots, leaving a rational number in the denominator. All solutions for binomial rationalisation in RD Sharma rely on this principle.
6. What are some common mistakes to avoid while solving difficult rationalisation problems from RD Sharma?
When tackling complex problems from RD Sharma Chapter 3, students should be cautious of these common errors:
- Using the wrong conjugate: Forgetting to change the sign of the second term in the binomial.
- Multiplication errors: Failing to correctly multiply every term in the numerator by the conjugate.
- Sign mistakes: Making errors with positive and negative signs during simplification after applying the identity.
- Incomplete simplification: Leaving the final answer with common factors in the numerator and denominator.
7. How does mastering rationalisation in Class 9 help in higher mathematics like in Class 11 and 12?
A strong grasp of rationalisation is fundamental for several advanced topics. In Class 11 and 12, this technique is frequently used in:
- Calculus: To evaluate limits of functions that result in indeterminate forms like 0/0.
- Complex Numbers: To express a fraction with a complex denominator in the standard a + ib form.
- Trigonometry: For simplifying complex trigonometric expressions and proving identities.
