About Radical Expressions:
Radicals allow us to reverse exponent operations. For example, squaring a number such as 5, or (-5) will give us 25. If we take the square root of 25, we get back to 5 or (-5). The same process occurs when we look at higher level roots. A cube root will undo cubing a number. A fourth root will undo raising a number to the fourth power.
Test Objectives
- Demonstrate a general understanding of radicals
- Demonstrate the ability to evaluate radical expressions
- Demonstrate the ability to work with fractional exponents
#1:
Instructions: Simplify each.
a) $$\sqrt[8]{1}$$
b) $$\sqrt[7]{-128}$$
c) $$\sqrt[4]{-16}$$
d) $$-\sqrt{225}$$
e) $$\sqrt[5]{-243}$$
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#2:
Instructions: Simplify each.
a) $$\sqrt{14^2}$$
b) $$\sqrt{(-19)^2}$$
c) $$-\sqrt[4]{(-13)^4}$$
d) $$\sqrt[3]{(-5)^3}$$
e) $$\sqrt[6]{(-243)^6}$$
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#3:
Instructions: Simplify each.
a) $$(-27)^\frac{1}{3}$$
b) $$(-81)^\frac{1}{2}$$
c) $$-(225)^\frac{1}{2}$$
d) $$(625)^\frac{1}{4}$$
e) $$(-64)^\frac{1}{3}$$
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#4:
Instructions: Simplify each.
a) $$\frac{x^{-1}z^2}{z^{-1}(x^{\frac{1}{2}}y^0z^{\frac{3}{2}})^{-2}}$$
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#5:
Instructions: Simplify each.
a) $$\frac{(x^{-\frac{5}{3}}x^{-\frac{1}{2}})^{\frac{2}{3}}}{x^{-\frac{5}{3}}}$$
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Written Solutions:
#1:
Solutions:
a) $$1$$
b) $$-2$$
c) $$not \hspace{.5em}real$$
d) $$-15$$
e) $$-3$$
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#2:
Solutions:
a) $$14$$
b) $$19$$
c) $$-13$$
d) $$-5$$
e) $$243$$
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#3:
Solutions:
a) $$-3$$
b) $$not \hspace{.5em}real$$
c) $$-15$$
d) $$5$$
e) $$-4$$
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#4:
Solutions:
a) $$z^6$$
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#5:
Solutions:
a) $$x^{\frac{2}{9}}$$
