Solving a Square Root Equation
What is the solution of 𝑥 + 4 + 6 = 7?
x4 67
6-5: Solving Square Root and
Other Radical Equations
x  4 1

Algebra 2
x4

2
 1
Isolate the Radical Expression
2
x  4 1
x  3
Subtract 4 from each side
Squaring can introduce
extraneous solutions.
Check your answers.
Complete Got It? #1 p. 391
 To solve an equation with a single rational power:
raise both sides of the equation to the
power of the reciprocal of that exponent.
3
1
3
6
The time (in t seconds) that it takes a pendulum to
complete one full swing is given by the formula :
Solving Equations with Radicals
What is the solution of 𝑥 2 = 5 and 6𝑥 + 9
Square Each Side
t  2
− 5 = −2?
L
g
where L is the length of the arm of the pendulum (in
cm.), and g is the acceleration due to gravity.
1
 6 x  9  3  5  2
3
x2  5
Remember to check for
extraneous solutions
2
3
2
 32 
3
x  5
 
x  5  25
x  2.92
3
2
3
𝒕 = 𝟐 𝒔𝒆𝒄
𝒈 = 𝟗𝟖𝟎 𝒄𝒎 𝒔𝒆𝒄𝟐
Find L, the length of
string.
3
1


  6x  9   3


6
x

9  27
Complete Got It? #2
p. 392
6 x  18
5
-11
x3
t  2
1
3
Solution on the next slide.
8  6 5b  3
Check:
?
8  6 5  3125   3
8  5b  3
6
2
2
Substitute the given values and solve for L.
 Raising each side to a power could introduce
extraneous solutions.
 Check all solutions in the original equation.
2
L

2
980
1
980    L
 
99.29  L
Suppose a ball on a string, swinging like a pendulum,
takes 2 seconds to complete one swing back and forth.
If g = 980 cm/sec2, find the length of the string.
Extraneous Solutions:
L
g
L
2  2
980
L
1
  
   980
3
1
6
The string is about
99.29 cm.
?
5b  5
5b   5 
8  6 15, 625  3
6
5b  15, 625
b  3125
85  3
No Solution
1
Checking Using a Calculator
6
Check 8 + 5𝑏 = 3 using a calculator.
10
 Graph each side of the
equation as an individual
equation.
Homework: p. 395 #9-33 odd
8
6
 𝑌1 = 8 + 5𝑏 and 𝑌2 = 3
6
 Use the INTERSECTION
function to find the
solution(s).
4
2
5
Solving Equations with Two Radicals
What is the solution(s) of 2 + 𝑥 − 6 − 𝑥 + 10 = 0?
2  x  6  x  10  0
2  x  6  x  10
2 
x6
 
2
x  10
Isolate one Radical Expression

2
Square Each Side
4  4 x  6  x  6  x  10
4 x  6  12
Homework: Complete WS 6-5G
Isolate 4 𝑥 − 6
x6  3

x6

2
  3
x6  9
x  15
2
Square Each Side
Subtract 6 from each side
2