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 the ability to evaluate a radical expression
- Demonstrate an understanding of the terms "perfect square" and "perfect cube"
- Demonstrate the ability to simplify a radical expression
#1:
Instructions: Evaluate each.
$$a)\hspace{.2em}\sqrt{121}$$
$$b)\hspace{.2em}\sqrt[3]{-64}$$
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#2:
Instructions: Evaluate each.
$$a)\hspace{.2em}{-}\sqrt[4]{625}$$
$$b)\hspace{.2em}\sqrt[5]{-243}$$
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#3:
Instructions: Determine if true or false.
a) 343 is a perfect square
b) 216 is a perfect cube
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#4:
Instructions: Simplify each.
Assume all variables represent real numbers (positive, negative, or zero)
$$a)\hspace{.2em}\sqrt{x^{10}y^4}$$
$$b)\hspace{.2em}\sqrt[3]{x^{15}y^{21}}$$
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#5:
Instructions: Simplify each.
Assume all variables represent real numbers (positive, negative, or zero)
$$a)\hspace{.2em}\sqrt{x^2 - 18x + 81}$$
$$b)\hspace{.2em}\sqrt[3]{x^3 - 9x^2 + 27x - 27}$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}11$$
$$b)\hspace{.2em}{-}4$$
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#2:
Solutions:
$$a)\hspace{.2em}{-}5$$
$$b)\hspace{.2em}{-}3$$
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#3:
Solutions:
a) false
b) true
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#4:
Solutions:
$$a)\hspace{.2em}|x^5| \cdot y^2$$
$$b)\hspace{.2em}x^5y^7$$
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#5:
Solutions:
$$a)\hspace{.2em}|x - 9|$$
$$b)\hspace{.2em}x - 3$$
