5.2.1 Perfect Square Equations

5.2.1 Perfect Square Equations

Multiple Choice

Find all the solutions for x when

x² + 9x - 36 = 0

• (x + 12)(x - 3)

• x = 12 and x = -3

• x = -12 and x = 3

• (x - 9)(x - 4)

Multiple Choice

Solve for the values of x:

(2x + 5)(5x - 2) = 0

• x= -5/2, x= -2/5

• x= -5/2, x= 2/5

• x= 5/2, x= 2/5

• x= 5/2, x= -2/5

Simplifying Radicals

Let's Review: Answer the following questions. Try doing so WITHOUT a calculator.

Multiple Choice

√64

• 8
• 32
• 7
• 9

Multiple Choice

√100

• 10
• 9
• 11
• 12

Multiple Choice

√16

• 4
• 8
• 2
• 32

Multiple Choice

√196

• 14
• 13
• 15
• 16

Multiple Choice

√25

• 5
• 12.5
• 4
• 50

Multiple Choice

√225

• 15
• 14
• 16
• 13

Multiple Choice

√169

• 13
• 12
• 11
• 14

Multiple Choice

√121

• 11
• 12
• 10
• 13

Multiple Choice

√49

• 7
• 6
• 8
• 24.5

Multiple Choice

√4

• 2
• 1
• 3
• 5

How to simplify a radical that is NOT a perfect square.

Multiple Choice

Example

• A

• B

• C

• D

Multiple Choice

• A
• B
• C
• D

Multiple Choice

Simplify: √31

• 3√1

• already simplified

• 1√3

• 15√2 + 1

Multiple Choice

Simplify the following radical: √24

• 2√6
• 4√6
• 2√12
• 3√8

Multiple Choice

Simplify the following radical: √32

• 3√2
• 4√8
• 16√2
• 4√2

How to solve quadratic equations in vertex form.

Open Ended

Without rewriting, determine the value(s) of x that make(s) the equation true:

(x-1)²=4

Open Ended

Without rewriting, determine the value(s) of x that make(s) the equation true:

(x-1)²=0

Open Ended

Without rewriting, determine the value(s) of x that make(s) the equation true:

(x-1)²=-4

Multiple Select

Solve the quadratic equation (there are two answers): x² = 16

• -4

• -8

• 4

• 8

What do the solutions mean?

How many solutions/roots/zeros/x-intercepts?

Here are two more examples

Rational vs. Irrational numbers AND exact vs. approximate form

Open Ended

Solve (2x-3)²=49 and give your answers in exact and approximate form.

Open Ended

Solve (5-10x)²=0 and give your answers in exact and approximate form.

Open Ended

Solve (7x-5)²=-2 and give your answers in exact and approximate form.

Open Ended

Solve (x+4)²=20 and give your answers in exact and approximate form.

Open Ended

Solve (x+2)²=-10 and give your answers in exact and approximate form.

Open Ended

Solve (x+11)²+5=5 and give your answers in exact and approximate form.

How does this relate to solving quadratics in vertex form?

Open Ended

Find the x-intercepts of y=(x+7)²-11.

Open Ended

Find the roots of y=(2x-1)²+6.

Open Ended

Find the zeros of y=(x-3)²