Math 9 Chapter 1 Lesson 9: Square root 1. Summary of theory 1.1. The concept of cubic roots - Define: The square root of a number a is the number x such that \(x^3=a\) Eg: The cube root of 8 is equal to 2 because \(2^3=8\). - Comment: Every number a has only one square root. - Note: From the definition of the square root, we have … [Read more...] about Math 9 Chapter 1 Lesson 9: Square root

# Math 9

## Math 9 Chapter 1 Lesson 8: Reducing the expression containing the square root

Math 9 Chapter 1 Lesson 8: Reducing the expression containing the square root 1. Summary of theory To reduce expressions containing square roots, we need to make appropriate use of known operations and transformations. 1.1. Example 1 Prove the equality \((1+\sqrt{2}+\sqrt{3})(1+\sqrt{2}-\sqrt{3})=2\sqrt{2}\) Solution guide In this problem, we can … [Read more...] about Math 9 Chapter 1 Lesson 8: Reducing the expression containing the square root

## Math 9 Chapter 1 Lesson 7: Simple transformation of expressions containing square roots (continued)

Math 9 Chapter 1 Lesson 7: Simple transformation of expressions containing square roots (continued) 1. Summary of theory 1.1. Desample of square root expression When transforming an expression containing a square root, one can use de-sampling of the square root expression. In a general way: With \(A\geq 0;B\neq 0\Rightarrow … [Read more...] about Math 9 Chapter 1 Lesson 7: Simple transformation of expressions containing square roots (continued)

## Math 9 Chapter 1 Lesson 6: Simple transformation of expressions containing square roots

Math 9 Chapter 1 Lesson 6: Simple transformation of expressions containing square roots 1. Summary of theory 1.1. Put the factor outside the square root sign - With \(a\geq 0;b\geq 0\), does \(\sqrt{a^2b}=a\sqrt{b}\)? - General: With two expressions A, B where \(B\geq 0\), we have \(\sqrt{A^2B}=|A|\sqrt{B}\), ie: If \(A\geq 0; B\geq 0\Rightarrow … [Read more...] about Math 9 Chapter 1 Lesson 6: Simple transformation of expressions containing square roots

## Math 9 Chapter 1 Lesson 5: Square Root Table

Math 9 Chapter 1 Lesson 5: Square Root Table 1. Summary of theory The square root table is divided into rows and columns. It is convention to name rows (columns) by the number listed in the first column (first row) of each page. The square roots of numbers written with no more than three digits from 1.00 to 99.9 are given in the table in columns 0 to 9. … [Read more...] about Math 9 Chapter 1 Lesson 5: Square Root Table

## Math 9 Chapter 1 Lesson 4: Relationship between division and squares

Math 9 Chapter 1 Lesson 4: Relationship between division and squares 1. Summary of theory 1.1. Theorem For non-negative a and positive b, we have: \(\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\) 1.2. Apply a. The rule of squaring a quotient To square a quotient \(\frac{a}{b}\), where a is not negative and b is positive, we can square the roots … [Read more...] about Math 9 Chapter 1 Lesson 4: Relationship between division and squares

## Math 9 Chapter 1 Lesson 3: Relationship between multiplication and squares

Math 9 Chapter 1 Lesson 3: Relationship between multiplication and squares 1. Summary of theory 1.1. Theorem - Theorem: For two non-negative numbers a and b, we have: \(\sqrt{a}.\sqrt{b}=\sqrt{ab}\) - Note: The theorem above can be extended to many non-negative numbers. 1.2. Apply a. Rule of square one product To square a product of … [Read more...] about Math 9 Chapter 1 Lesson 3: Relationship between multiplication and squares

## Math 9 Chapter 1 Lesson 2: Square roots and square root equality constants

Math 9 Chapter 1 Lesson 2: Square roots and square root equality constants 1. Summary of theory 1.1. Square root With A being an algebraic expression, \(\sqrt{A}\) is called the square root of A, and A is called a radical expression, or an expression under the radical sign. \(\sqrt{A}\) determines (or makes sense) when A has a non-negative … [Read more...] about Math 9 Chapter 1 Lesson 2: Square roots and square root equality constants

## Math 9 Chapter 1 Lesson 1: Square Root

Math 9 Chapter 1 Lesson 1: Square Root 1. Summary of theory 1.1. Arithmetic square root - The square root of a non-negative number a is the number x such that \(x^2=a\) - For a positive number a, the number \(\sqrt{a}\) is called the arithmetic square root of a. - The number 0 is also called the arithmetic square root of 0 . 1.2. Compare two … [Read more...] about Math 9 Chapter 1 Lesson 1: Square Root