Lessons 9'1

1
Lessons 9.1 9.2Understanding Squares and
Square Roots
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The square root symbol is called a
radical.v25 v25 5, because 52 25.The
expression under the radical symbol is called the
radicand.
3
Square Roots have two roots. Example v9 3
and -3 v9 3
4
Radical Expressions
Evaluate
when a 7, b 8, c 1
5
Solving x2 d

• If dgt0, then x2 d has two solutions. x vd,
  -vd
• If d0, then x2 d has one solution. x 0
• If dlt0, then x2 d has no solutions.
• Why does a negative number have no solutions?

6
Solving equations with squares Another
inverse operation to get rid of a square take
the square root.
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Solving equations with squares
3y2 192
3y2 1923 3
y2 64
v(y2) v 64
y 8
8
Solving equations with squares
8y2 16 24
8y2 16 16 24 16
8y2 408 8
y2 5
v(y2) v 5
y v 5
9
Simplifying Radicals a. vmv n
b. Factor out the largest square root
factor. c.
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Simplifying Radicals
v112
v16v 7
4v7
11
Simplifying Radicals
v50
v25v 2
5v2
12
Simplifying Radicals
v128
v16v8
4v4v2
4(2)v2
8v2
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Properties of Square Roots

• No perfect square factors other than 1 are in the
  radicand.
• No fractions are in the radicand
• No radicals appear in the denominator.