Solving Radical Equations

Unit 4, Lesson 10February 16th, 2015

Do Now (3 mins) Solve for x.

a)

b)

c)

d)

e)

f)

g)

26 = 8 + v

−15 + n = −9

9x − 7 = −7

8n + 7 = 31

5p −14 = 8p + 4

n − 3n = 14 − 4n

4x + 27 = 3x

StandardsA.SSE-Seeing Structure in Expressions

Interpret the structure of expressions.

1. Interpret expressions that represents a quantity in terms of its context.

2. Ue the structure of an expression to identify ways to rewrite it.

A.REI-Reasoning with Equations and Inequalities

Understand solving equations as a process of reasoning and explain the reasoning.

2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

ObjectiveHuskies will be able to solve equations containing radicals and identify extraneous solutions.

Huskies will show mastery by earning a 3 out of 4 on the exit slip.

VocabularyRadical Equation- An equations in which a variable or an expression containing a variable is inside the radical sign.

Extraneous Roots- A solution to an equation that SEEMS to be right, but when we check it (substitution) it is not right.

x + 9 = 14

Review!Putting it Together

x( )2 =

25( )2 =

7( )2 =

Working with Radicals

x + 9 = 14

Simplify each radical expression by multiplying or dividing.

Check for extraneous solutions

Working with RadicalsSo what are the steps to solve radical equations

1.

2.

3.

4.

You Try

7 + x = 10

Simplify each radical expression by multiplying.

2x − 3 = x +1

2x − 5 = 1 x = 2x

Partner Work

5 = x − 3

Solve each radical equation. Check each answer by substituting the answer back into the original equation.

n + 9 = 1

5 = 1− x 1x= 2

Relate itThe formula shows the relationship between mass, mvelocity in meters per second.

v = 2KEm

•What is the kinetic energy of a traveling at a velocity of

•What is the kinetic energy of a traveling at a velocity of

Summary of the Math• To solve radical equations, you must use the identity

• Begin by isolating the radicals on one side. Combine like terms on each side if possible.

• Get rid of the square root by squaring both sides.

• Use properties of equality to finish solving the equations.

• Use substitution to check your answers. If one is wrong even though your solution process is correct, it is an extraneous solution and should not be included in your answer.

x( )2 = x

Independent/Group Practice

• Complete page 18 of the Pearson Exercises

Exit SlipUnit 4, Lesson 10

1x= 2

2x − 5 = 7 3= x −12

t + 2 t = 12

EC: 5 + 2x = 2 2x −1

Solve each radical equation. Check your answer using substitution (plugging back your answer).