Using Your Algebra Skills 8: Radical Expressions
___________________________ – an expression that has a root or radical (√ ).
___________________ – the number, variable, or algebraic expression under the radical sign.
_________________ – the number that tells which root to find. If no index is shown it is understood to
be an index of 2 or square root.
index→
𝑎
√𝑛 ←radicand
To simplify a square root: Method 1
 Factor the radicand completely.
 Look for pairs of factors that are the same.
 For every pair of matching factors, cross them out, write the number outside the radical and leave
the other factors under the radical.
 Multiply the factors under the radical to become the new radicand.
To simplify a square root: Method 2
 Factor the radicand looking for perfect square factors.
 Separate the radicals with the perfect square factors and the non-perfect square factors.
 Take the square roots of the perfect squares and write the number in front of the other radical.
Perfect squares:
12 = 1
112 = 121
212 = 441
22 = 4
122 = 144
222 = 484
32 = 9
132 = 169
232 = 529
42 = 16
142 = 196
242 = 576
52 = 25
152 = 225
252 = 625
62 = 36
162 = 256
262 = 676
72 = 49
172 = 289
272 = 729
82 = 64
182 = 324
282 = 784
92 = 81
192 = 361
292 = 841
102 = 100
202 = 400
302 = 900
Geometry Lesson Using Your Algebra Skills 8: Radical Expressions
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Example 1: Simplify each radical expression.
a. √200
b. √27
c. √120
d. √75
e. √50
Geometry Lesson Using Your Algebra Skills 8: Radical Expressions
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Example 2: Find the product of each. Write your answer in simplest form.
a. (4√3)(√7)
b. (3√2)(4√3)
c. (5√10)(7√10)
d. (10√5)(4√50)
Geometry Lesson Using Your Algebra Skills 8: Radical Expressions
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Example 3: Simplify each radical expression.
a. √40𝑥 3 𝑦 4
b. √50𝑎3 𝑏 5
c. √200𝑥𝑦 2 𝑧 3
Example 4: Draw a diagram and solve each problem. Leave your answers in simplest radical form.
a. If the lengths of the two legs of a right triangle are 3 and 15, what is the length of the hypotenuse?
b. Find the length of the diagonal of a rectangle with length of 7 cm and width of 12 cm.
Homework: p. 474 => 1 - 21
Geometry Lesson Using Your Algebra Skills 8: Radical Expressions
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