extracting cube roots mentally

Extracting Cube Roots MentallyPresented by Grey Matters Mental Gym

http://members.cox.net/beagenius/

Extracting Cube Roots Mentally

• A cube is a number multiplied by itself twice more. For example, 3 cubed (33) is 3 * 3 * 3, or 27.

• A cube root is the number that, when cubed, results in a given number. For example, the cube root of 27 (3√27) is 3.


• Have a spectator choose any number from 1 to 100, cube it with their calculator and give you the answer.

Imagine being able to figure the cube root of that number in your head!

Extracting Cube Roots MentallyRequirements

• Calculator

Spectator


• To be able to extract cube roots mentally, you must know the first 10 cubes mentally:

• 13=1 23=8• 33=27 43=64• 53=125 63=216• 73=343 83=512

93=729 103=1000


• Note that no two cubes end in the same digit:

• 13=1 23=8• 33=27 43=64• 53=125 63=216• 73=343 83=512• 93=729 103=1000


• Also notice that the cubes of 1, 4, 5, 6, 9 and 0 end in those same digits:

• 13=1 23=8

33=27 43=64• 53=125 63=216• 73=343 83=512• 93=729 103=1000


• Finally, notice that 23 ends in 8, 83 ends in 2, 33 ends in 7 and 73 ends in 3:

13=1 23=8• 33=27 43=64• 53=125 63=216• 73=343 83=512• 93=729 103=1000


If you’re given one of the cubes you’ve memorized from this chart, simply give the cube root you’ve remembered.


• If you’re given a number that ranges from 1,000 (103) to 1,000,000 (1003), you’ll need to go through the following steps.


First, split the number into two parts at the comma. As an example, let’s say you’re given the number 39,304. You would mentally split it into “39” and “304”.


• Next, focusing on the number to the left of the comma, ask yourself, “What is the largest cube that is equal to or less than that number?”

• In our example, the largest cube that is equal to or less than 39 (the number to the left of the comma) is 27.


• Recall the cube root of this number, and that will be the tens digit of the answer.

• In our example, we found that 27 was the largest cube less than or equal to 39. Since we know that the cube root of 27 is 3 (3√27=3), we now know our answer is in the 30s somewhere.


Now, focus on the number to the right of the comma. In our example of 39,304, this would be the “304”.


• Look at just the rightmost digit, and ask yourself, “Which digit, from 0-9, when cubed, would result in that digit?” This will be the ones digit of the answer.

• In our example of 39,304, we see that the rightmost digit is a 4. Remembering that 4 is the only cube that ends in a 4 (43=64), this must be the ones digit of the answer!


• Once you know both the tens digit and the ones digit of the answer, put them together and you have the cube root.

In our example, we determined that the answer for “39,304” is in the 30s, and that it ends in 4, so we give 34 as the cube root!


• Other examples:• What is 3√50,653? Because “50” is

greater than 27 (33), and less than 64 (43), we know the answer is in the 30s. Because “653” ends in 3, we know that the answer must end in 7, as only 73 (343) ends in 3. Therefore, 3√50,653=37.


• Other examples:• What is 3√314,432? Because “314” is

greater than 216 (63), and less than 343 (73), we know the answer is in the 60s. Because “432” ends in 2, we know that the answer must end in 8, as only 83 (512) ends in 2. Therefore, 3√314,432=68.


• Other examples:• What is 3√704969? Because “704” is

greater than 512 (83), and less than 729(93), we know the answer is in the 80s. Because “969” ends in 9, we know that the answer must end in 9, as only 93 (729) ends in 9. Therefore, 3√704969=89.