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Solve each equation.
1. x2 = 64
x = 8 and - 8
Algebra 2
Section 6.1
Square Roots
take the square root of both sides
2. 4n2 = 64
n2 = 16 divide both sides by 4
n = 4 and - 4 take the square root of both sides
3. a2 – 7 = 22
a2 = 29 add 7 to both sides
a  5.4 and – 5.4 take the square root of both sides
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4. 6y2 + 14 = 434
-14
-14
subtract 14 from both sides
6y2 = 420
y2 = 70 divide both sides by 6
y 8.4 and – 8.4
5. 9a2 = 2a2 + 294
-2a2
-2a2
subtract 2a2 from both sides
7a2 = 294
a2 = 42 divide both sides by 7
a  6.5 and – 6.5
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6. 3x2 – 86 = x2 + 86
-x2 +86
-x2 +86
subtract x2 and add 86 to both sides
2x2 = 172
x2 = 86 divide both sides by 2
x 9.3 and – 9.3
7. 5x2 – 1 = 4x2 + .21
- 4x2
- 4x2
subtract 4x2 from both sides
x2 – 1 = .21
+1
+1 add 1 to both sides
x2 = 1.21
x = 1.1 and – 1.1
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rational number: a number that can be written as a fraction
Determine whether each number is rational or irrational.
Number
3. 888
Answer
rational
all repeating decimals can be written as a fraction
5.37
rational
all terminating decimals can be written as a fraction
2
9
irrational
169
9
rational
99
irrational
 6.25
4.3131131113...
rational
irrational
Reason
2/9 is not a perfect square
169 is a perfect square = (13/3)2
9
99 is not a perfect square
6.25 is a perfect square = (2.5)2
non-terminating / non-repeating = irrational
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Determine whether each number is rational or irrational.
1. 5.282282228
= irrational non-terminating / non-repeating
2.
169
= rational
it is 13
3.  400
= rational
it is - 20
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4. 87.6543
= rational
terminating
5.  3000
= irrational
49
6.
81
= rational
non-terminating / non-repeating
it is 7/9
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Algebra 2
Section 6.1
Assignment
Solve each equation.
1.) y2 = 3
2.) c2 + 6 = 21
3.) 900 = x2
4.) 16n2 = 7n2 + 4
Solve each equation. Approximate solutions to the nearest hundredth.
5.) 3y2 = 195
6.) 25c2 – 7 = 9
7.) 4n2 = 20n2 – 9
8.) 6n2 + 75 = n2 + 455
Determine whether each number is rational or irrational.
9.) 0.123123123….
10.) 7.65765765….
11.)
47
12.)  75
13.) 19. 4747
14.)
2,025
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