3. A 10-foot ladder leans against a wall with its foot braced 3 feet from wall’sbase. How far up the wall does the ladder reach?
4.
A square picture frame occupies an area of 112 f
2
. What is the length of each side of the picture in
simplified radical form
?
Show your work
.
1

Algebra I Quarter 4 Exam
A = a^2
112 = a^2
sqrt 112 = a
sqrt 16 * sqrt 7 = a
4 sqrt 7 = a
=4 sqrt7
Simplify each radical expression. Leave in radical form. Show your work
. (because of the spacing it was
hard to put the work directly under the problem)
5.
5
45
n
6.
√
75
+
√
3
7.
7( 14
3)
=3n^2sqrt5n
= sqrt(3 * 5^2) + sqrt(3)
Sqrt(7)*(sqrt(14)sqrt(3)
Sqrt(7)(sqrt (7) sqrt(2)+sqrt(3)
=7sqrt2+sqrt21
= sqrt(3) * sqrt(5^2) + sqrt(3)
= sqrt(3) * 5 + sqrt(3)
= 5 * sqrt(3) + sqrt(3)
= (5 + 1) * sqrt(3)
=6sqrt3
sqrt 45n^5 = sqrt 5*9n^4n = 3n^2 sqrt 5n
2

Algebra I Quarter 4 Exam
S
implify the rational expressions.
State any excluded values.
Show your work
.
8.
Factor 3 out of 3x-6
=3
9
.
factor the denominator, cancel out common factors
=1/x+5
Multiply or divide.
Show your work
.

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