A. Working with Cube Roots
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A. Working with Cube Roots
A perfect cube is formed by multiplying the same rational number three times. The cube root of a perfect cube gives the original rational number.
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Example 1 |
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In this example, 64 is a perfect cube, formed by multiplying the number 4 three times. The cube root of 64 is the original number, 4. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «semantics» «mstyle mathvariant=¨normal¨ mathsize=¨12.0pt¨ mathcolor=¨#000000¨» «mtable columnlines=¨none none¨ rowlines=¨none none none none none¨» «mtr» «mtd columnalign=¨right¨» «/mtd» «/mtr» «/mtable» «/mstyle» «/semantics» «/math» |
| For square roots, the index of 2 is implied and rarely written.
As such, «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mn»2«/mn»«/mroot»«mo»=«/mo»«msqrt»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/msqrt»«mo»=«/mo»«mi»x«/mi»«/math» for positive values of x. |
, is the opposite operation of the exponent 3.
Key Lesson Marker
In general, «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot»«mi»x«/mi»«mn»3«/mn»«/mroot»«mo»=«/mo»«mi»x«/mi»«/math».