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Radical Expressions and Equations

This chapter provides a comprehensive overview of key mathematical concepts, including the Pythagorean Theorem and operations with radical expressions. Students will learn to identify right triangles, solve problems using the theorem, simplify radicals, and solve radical equations. Additionally, the chapter covers graphing square root functions and explores trigonometric ratios in right triangles. These fundamental concepts aim to prepare students for more advanced applications in geometry and algebra.

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Radical Expressions and Equations

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  1. Radical Expressions and Equations Chapter 10

  2. 10.1 The Pythagorean Theorem • Pg. 614 – 618 • Obj: Learn how to solve problems using the Pythagorean Theorem and identify right triangles. • Content Standard: G.SRT.8

  3. 10.1 The Pythagorean Theorem • Hypotenuse – the longest side of a right triangle – opposite of the right angle (c) • Leg – one of the shorter sides of a right triangle – one of the two sides that form the right angle (a and b) • Pythagorean Theorem

  4. 10.1 The Pythagorean Theorem • Conditional – an if-then statement • Hypothesis – the part following the “if” • Conclusion – the part following the “then” • Converse – switches the hypothesis and the conclusion • Converse of the Pythagorean Theorem –

  5. 10.2 Simplifying Radicals • Pg. 619 – 625 • Obj: Learn how to simplify radicals involving products and quotients. • Content Standard: Prepares for A.REI.2

  6. 10.2 Simplifying Radicals • Radical Expression – an expression that contains a radical • Multiplication Property of Square Roots • Division Property of Square Roots

  7. 10.3 Operations with Radical Expressions • Pg. 626 – 631 • Obj: Learn how to simplify sums, differences, products, and quotients of radical expressions. • Content Standard: Prepares for A.REI.2

  8. 10.3 Operations with Radical Expressions • Like radicals – radicals that have the same radicand • Unlike radicals – radicals that have different radicands • Conjugates

  9. 10.4 Solving Radical Equations • Pg. 633 – 638 • Obj: Learn how to solve equations containing radicals and identify extraneous solutions. • Content Standard: A.REI.2

  10. 10.4 Solving Radical Equations • Radical Equation – an equation that has a variable in a radicand • Extraneous Solution – an apparent solution that does not satisfy the original equation

  11. 10.5 Graphing Square Root Functions • Pg. 639 – 644 • Obj: Learn how to graph square root functions and translate graphs of square root functions. • Content Standards: F.IF.7.b and A.CED.2

  12. 10.6 Trigonometric Ratios • Pg. 645 – 651 • Obj: Learn how to find and use trigonometric ratios. • Content Standards: G.SRT.8 and G.SRT.6

  13. 10.6 Trigonometric Ratios • Trigonometric Ratios – ratios of the side lengths of a right triangle • Sine = opposite/hypotenuse • Cosine = adjacent/hypotenuse • Tangent = opposite/adjacent

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