- Chapter No.1 Introduction to Biology
- Chapter No. 2 Solving a Biological Problem
- Chapter No.3 Biodiversity
- Chapter No.4 Cells and Tissues
- Chapter No.5 Cell Cycle
Exercise 4.3 involves various tasks related to simplifying surds, simplifying algebraic expressions, and combining similar terms. Let’s take a closer look at each question:
Q1. Express each of the following surds in the simplest form
In this part of the exercise, you will be given surds, which are expressions containing roots (e.g., square roots, cube roots), and you are required to simplify them to their simplest form. To do this, you will need to find the factors of the radicand (the number inside the root) and determine if any perfect square factors can be extracted. The objective is to express the surd with no more square roots or cube roots. For example, if you have √12, you can simplify it to 2√3 because 12 can be expressed as 2 * 2 * 3, and we can extract a perfect square factor of 2.
Q2. Simplify the expression
In this part, you will be given algebraic expressions, and you need to simplify them by performing arithmetic operations like addition, subtraction, multiplication, and division. This will involve combining like terms, applying the distributive property, and following the order of operations (PEMDAS). The goal is to obtain a simplified expression that has fewer terms and is easier to work with. For instance, if you have the expression 3x + 2x – 5x, you can simplify it to 0 because the x terms cancel each other out.
Q3. Simplify by combining similar terms
Similar to Q2, in this part, you will also be given algebraic expressions, but the emphasis will be on combining similar terms specifically. This means you need to identify terms that have the same variables raised to the same powers and then combine them. For example, if you have the expression 4x + 2y – 3x + 7y, you can simplify it to x + 9y by combining the x terms and the y terms.
In conclusion, Exercise 4.3 is a comprehensive set of problems that will test your skills in simplifying surds, simplifying algebraic expressions through arithmetic operations, and combining similar terms to obtain simplified expressions. By mastering these concepts and techniques, you will strengthen your algebraic manipulation abilities, which are vital for tackling more advanced mathematical challenges in algebra and other mathematical disciplines.