Transcript Solve Radical Equations

Five-Minute Check (over Lesson 6–6)
CCSS
Then/Now
New Vocabulary
Key Concept: Solving Radical Equations
Example 1: Solve Radical Equations
Example 2: Solve a Cube Root Equation
Example 3: Standardized Test Example: Solve a Radical
Equation
Key Concept: Solving Radical Inequalities
Example 4: Solve a Radical Inequality
Over Lesson 6–6
A.
B.
C.
D.
Over Lesson 6–6
A. 12
B. 8
C. 4
D. 2
Over Lesson 6–6
A.
B.
C.
D.
Over Lesson 6–6
A. 2w 2
B. 2w
C. w 2
D.
Over Lesson 6–6
A.
B.
C. 5
D. 10
Over Lesson 6–6
The equation
gives the approximate
energy output y in kilocalories per day (kcal/day)
for a reptile with a body mass m kilograms. The
average mass of an alligator is 360 kilograms. Find
the energy output of a reptile this size. Round your
answer to the nearest tenth.
A. 82.6 kcal/day
B. 156.8 kcal/day
C. 826.5 kcal/day
D. 1568.1 kcal/day
Content Standards
A.SSE.2 Use the structure of an expression
to identify ways to rewrite it.
Mathematical Practices
4 Model with mathematics.
You solved polynomial equations.
• Solve equations containing radicals.
• Solve inequalities containing radicals.
• radical equation
• extraneous solution
• radical inequality
Solve Radical Equations
A. Solve
.
Original equation
Add 1 to each side to
isolate the radical.
Square each side to
eliminate the radical.
Find the squares.
Add 2 to each side.
Solve Radical Equations
Check
Original equation
?
Replace y with 38.

Simplify.
Answer: The solution checks. The solution is 38.
Solve Radical Equations
B. Solve
.
Original equation
Square each side.
Find the squares.
Isolate the radical.
Divide each side by –4.
Solve Radical Equations
Square each side.
Evaluate the squares.
Original equation
Check
Replace x with 16.
Simplify.
Evaluate the square roots.

Answer: The solution does not check, so there is no
real solution.
A. Solve
A. 19
B. 61
C. 67
D. no real solution
.
B. Solve
A. 2
B. 4
C. 9
D. no real solution
.
Solve a Cube Root Equation
In order to remove the
power, or cube root, you must
first isolate it and then raise each side of the equation to
the third power.
Original equation
Subtract 5 from
each side.
Cube each side.
Evaluate the cubes.
Solve a Cube Root Equation
Subtract 1 from each side.
Divide each side by 3.
Check
Original equation
Replace y with –42.
Simplify.

The cube root of –125 is –5.
Add.
Answer: The solution is –42.
A. –14
B. 4
C. 13
D. 26
Solve a Radical Equation
A
m = –2
B
m=0
C
m = 12
D
m = 14
Solve a Radical Equation
Original equation
Add 4 to each side.
Divide each side by 7.
Raise each side to the sixth
power.
Evaluate each side.
Subtract 4 from each side.
Answer: The answer is C.
A. 221
B. 242
C. 266
D. 288
Solve a Radical Inequality
Since the radicand of a square root must be greater
than or equal to zero, first solve 3x – 6  0 to identify
the values of x for which the left side of the inequality is
defined.
3x – 6  0
3x  6
x2
Solve a Radical Inequality
Original inequality
Isolate the radical.
Eliminate the radical.
Add 6 to each side.
Divide each side by 3.
Answer: The solution is 2  x  5.
Solve a Radical Inequality
Check
Test some x-values to confirm the solution. Let
Use three test values: one less than 2,
one between 2 and 5, and one greater than 5.
Only the values in the interval 2  x  5 satisfy the
inequality.
A.
B.
C.
D.