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Step 6Evaluating the Cube Root Part 2: Left Hand Side
From step 4, we split the cube root into 2 parts, evaluating both sides of the expression to determine the cube root. We already evaluated the right-hand side of the expression, now it's time to evaluate the left hand side. Using our example, we split the number 50,653 into two parts: 50 and 653. In this step, we will evaluate the 50, yielding the 10's digit of our extracted cube root.
To determine the 10's digit of our cube root, we take our left hand side (50) and pick the 2 cubes that it falls between. From our list of cube roots:
03 = 0
13 = 1
23 = 8
33 = 27
43 = 64
53 = 125
63 = 216
73 = 343
83 = 512
93 = 729
We see that our number (50) falls between 33 and 43. We shall pick the lower number, and that becomes our cube root's 10's digit.
With the 1's digit evaluating to 7 and the 10's digit evaluating to 3, it is now easy to see that the cube root of 50,653 is 37. You can check it on a calculator, if you so wish. Neat, huh?
To determine the 10's digit of our cube root, we take our left hand side (50) and pick the 2 cubes that it falls between. From our list of cube roots:
03 = 0
13 = 1
23 = 8
33 = 27
43 = 64
53 = 125
63 = 216
73 = 343
83 = 512
93 = 729
We see that our number (50) falls between 33 and 43. We shall pick the lower number, and that becomes our cube root's 10's digit.
With the 1's digit evaluating to 7 and the 10's digit evaluating to 3, it is now easy to see that the cube root of 50,653 is 37. You can check it on a calculator, if you so wish. Neat, huh?
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Jul 22, 2008. 6:40 AM
jeff-o
says:
jeff-o
says:
Well that's pretty darned nifty. If I'd known this trick in high school, well, I'd probably be an even bigger geek. ;)
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