-â-243. 5. EX2: Write in radical form and simplify. Assume all variable expressions represent positive real numbers. [a.] 163/4. [b.] (-64)2/3. [c.]...
R.7 // Radical Expressions An alternative notation for expressing roots is to use: ____________________ Suppose that: ______________________, then also,
in radical symbol:
EX1: Write each root using exponents and evaluate. 3
4 [b.] - √ 10,000
4
[e.]
[a.] √27
[d.] √-81
3
[c.] √-216
125
3
5
[f.] - √-243
512
EX2: Write in radical form and simplify. Assume all variable expressions represent positive real numbers. [a.] 163/4
[b.] (-64)2/3
[c.] -1213/2
[d.] y7/8
[e.] 7z4/5
[f.] 12q1/4
[g.] (5x + 2y)1/6
EX3: Write in exponential form. Assume all variable expressions represent positive real numbers. 7
4
[a.] √n3
[d.] -2
5
3
[c.] 15( √r)4
[b.] √10x
8
3
[e.] √r2 + s4
(3x2 )
If n is an even positive integer, then: If n is an odd positive integer, then: EX4: Simplify each expression. [a.] √z6
[b.]
5
[f.]
[e.] √m10
7
t7
[c.]
2
(3x - 4)
81r8 s10
[g.] √x2 - 10x + 25
[d.]
4
4
(-3)
Rules for Radicals product rule:
quotient rule:
power rule: EX5: Simplify. Assume all variables represent positive real numbers. [a.] √5 · √45
[d.]
6
a b12
5
5
[b.] √n3 · √n2
[e.]
11
[c.]
5 4
√17
169
6
√8
[f.]
Simplified Radicals [1.] The radicand has: _______________________________________________________ [2.] The radicand has: _______________________________________________________ [3.] No denominator contains: _________________________________________________ [4.] Exponents in the radicand and the index: ______________________________________ [5.] All: _________________________________________________________________ EX6: Simplify each radical. [a.] √288
3
[b.] -8 √125
[c.]
3
128a6 b8 c10
DEF: like radicals = __________________________________________________________ like:
unlike:
EX7: Add or subtract, as indicated. Assume all variables represent positive real numbers. [a.] 14√5pq - 11√5pq