cube roots a is a cube root of b if and only if example 1 2 is a cube root of 8, since - 2 is a cube...
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Cube Roots
3a b
• a is a cube root of b if and only if
• Example 1
2 is a cube root of 8, since 32 8
- 2 is a cube root of - 8, since 32 8
• Note a key difference between square roots and cube roots:
Square Root
23 9
23 9
The number 9 has two square roots, -3 and 3.
Cube Root
The number 8 has one cube root, 2.
32 8
• Recall that when using radical notation, the square root is equal to the principal (nonnegative) square root.
3 3a a
• Also, when simplifying a square root, it was sometimes necessary to use an absolute value sign.
• The cube root is much simpler, and is defined as:
2a a
• Example 2
Evaluation Reasoning
3 64 4 34 64
3 8 2 32 8
• Example 3
2x
Simplify
33 2x
33 2x
• Example 4
Simplify 3 327x
First write the radicand as a quantity cubed.
3 327x 3 33 3 x
33 3x
3x
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