Exercise 4.3: Introduction to Algebraic Expressions

The chapter Algebraic Expressions in the 9th class science textbook of Punjab Textbook Board includes the following:

Exercise 4.3:Introduction to Algebraic Expressions: This section introduces the concept of algebraic expressions, which are mathematical expressions that involve variables and constants.
Simplifying Algebraic Expressions: This section discusses the various methods of simplifying algebraic expressions, such as combining like terms, factoring, and using the distributive property.
Applications of Algebraic Expressions: This section discusses the various applications of algebraic expressions in real-world problems, such as solving equations, inequalities, and word problems.

Exercise 4.3 of this chapter focuses on the simplification of surds. A surd is an algebraic expression that contains an irrational number, such as a square root.

The following are some of the questions that are asked in Exercise 4.3:

Simplify:
√2 + √2
7√5 – 3√5
√20 + √45
√8 – √32
Simplify:
√(32a²)
√(16b²)
√(100c²)
Simplify:
√(a²/b²)
√(b²/a²)
√(a³/b³)
√(b³/a³)
Simplify:
√(25a² + 9b²)
√(36a² – 4b²)
√(a² + b² + c²)
√(a² + b² – c²)
Simplify:
√(a² + b²) + √(c² + d²)
√(a² + b²) – √(c² + d²)

The solutions to these questions can be found in the textbook.

Exercise 4.3: Introduction to Algebraic Expressions, t recognize the surds and their application, t explain the surds of second order, Use basic operations on surds of second order,

Here is the Introduction maths 9th class Exercise 4.3 Punjab text book surds and applications.

Question 1: Simplify:
- 5√2 + 3√2 (ii) 7√5 – 3√5 (iii) √20 + √45 (iv) √8 – √32
Solution:
5√2 + 3√2 = (5 + 3)√2 = 8√2 (ii) 7√5 – 3√5 = (7 – 3)√5 = 4√5 (iii) √20 + √45 = √(4 × 5) + √(9 × 5) = 2√5 + 3√5 = 5√5 (iv) √8 – √32 = √(4 × 2) – √(16 × 2) = 2√2 – 4√2 = -2√2
Question 2: Simplify:
√(32a²) (ii) √(16b²) (iii) √(100c²)
Solution:
√(32a²) = 4a (ii) √(16b²) = 4b (iii) √(100c²) = 10c
Question 3: Simplify:
√(a²/b²) (ii) √(b²/a²) (iii) √(a³/b³) (iv) √(b³/a³)

Solution:

√(a²/b²) = √(a/b)² = a/b (ii) √(b²/a²) = √(b/a)² = b/a (iii) √(a³/b³) = √(a/b)³ = a/b (iv) √(b³/a³) = √(b/a)³ = b/a

Question 4: Simplify:

√(25a² + 9b²) (ii) √(36a² – 4b²) (iii) √(a² + b² + c²) (iv) √(a² + b² – c²)

Solution:

√(25a² + 9b²) = 5a√(5 + 3b/a) (ii) √(36a² – 4b²) = 6a√(9 + b/a) (iii) √(a² + b² + c²) = √(a² + b² + c²) = a + b + c (iv) √(a² + b² – c²) = √(a² + b²) + √(c²) = a + b + c

Question 5: Simplify:

√(a² + b²) + √(c² + d²) (ii) √(a² + b²) – √(c² + d²)

Solution:

√(a² + b²) + √(c² + d²) = √[(a² + b²) + (c² + d²)] = √(a² + b² + c² + d²) (ii) √(a² + b²) – √(c² + d²) = √[(a² + b²) – (c² + d²)] = √(a² – c² + b² – d²)

Questions & Answers

Here is a conclusion about Algebraic ExpressionsExercise 4.3: Introduction to Algebraic Expressions class 9th science Punjab text book:

Algebraic Expressions Exercise 4.3 in the 9th class science textbook of Punjab Textbook Board focuses on the simplification of surds. A surd is an algebraic expression that contains an irrational number, such as a square root.Exercise 4.3:

The exercise includes a variety of questions that test the student’s ability to simplify surds using a variety of methods, such as combining like terms, factoring, and using the distributive property.

The exercise also includes some questions that require the student to apply their knowledge of surds to solve real-world problems.

Overall, Algebraic Expressions Exercise 4.3 is a challenging but rewarding exercise that can help students improve their skills in simplifying algebraic expressions involving surds.

Conclusion

Here are some tips for students who are struggling with Algebraic Expressions Exercise 4.3:

Start by carefully reading the instructions for each question.
Make sure you understand the meaning of all the terms used in the question.
Work through the problem step-by-step, carefully following the instructions.
If you get stuck, try to break the problem down into smaller, more manageable steps.
Don’t be afraid to ask for help from a teacher or classmate.Exercise 4.3:

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