# Extracting Fifth Roots Mentally

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01-Sep-2014Category

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How do you find fifth roots, using only your mind? This slideshow will show you how!

### Transcript of Extracting Fifth Roots Mentally

- Extracting Fifth Roots Mentally
- Presented by Grey Matters Mental Gym

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

- Extracting Fifth Roots Mentally
- A fifth power is a number multiplied by itself four more times. For example, 3 to the fifth power (3 5 ) is 3 * 3 * 3 * 3 * 3, or 243.

- A fifth root is the number that, when taken to the fifth power, results in a given number. For example, the fifth root of 243 ( 5 243) is 3.

- Extracting Fifth Roots Mentally
- Have a spectator choose any number from 1 to 100, taking it to the fifth power with their calculator and give you the answer.

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

- Extracting Fifth Roots Mentally Requirements
- A calculator capable of displaying 11 or more digits

- Spectator

- Extracting Fifth Roots Mentally
- To be able to extract fifth roots mentally, you must know the first 10 mentally:

- 1 5 =1 2 5 =32

- 3 5 =243 4 5 =1,024

- 5 5 =3,125 6 5 =7,776

- 7 5 =16,807 8 5 =32,768

- 9 5 =59,049 10 5 =100,000

- Extracting Fifth Roots Mentally
- Note that each fifth power ends in the same digit as its fifth root:

- 1 5 = 1 2 5 =3 2

- 3 5 =24 3 4 5 =1,02 4

- 5 5 =3,12 5 6 5 =7,77 6

- 7 5 =16,80 7 8 5 =32,76 8

- 9 5 =59,04 9 10 5 =100,00 0

- Extracting Fifth Roots Mentally
- If youre given one of the fifth power youve memorized from this chart, simply give the fifth root youve remembered.

- Extracting Fifth Roots Mentally
- If youre given a number that ranges from 100,000 (10 5 ) to 10,000,000,000 (100 5 ), youll need to go through the following steps.

- Extracting Fifth Roots Mentally
- First, split the number into two parts, with the right half consisting of the 5 rightmost digits, and the left half consisting of the rest. As an example, lets say youre given the number 11,881,376. You would mentally split it into 118 and 81,376.

- Extracting Fifth Roots Mentally
- Next, focusing on the number to the left of the comma, ask yourself, What is the largest fifth power that is equal to or less than that number?

- In our example, the largest fifth power that is equal to or less than 118 is 32.

- Extracting Fifth Roots Mentally
- Recall the fifth root of this number, and that will be the tens digit of the answer.

- In our example, we found that 32 was the largest fifth power less than or equal to 118. Since we know that the fifth root of 32 is 2 ( 5 32=2), we now know our answer is in the 20s somewhere.

- Extracting Fifth Roots Mentally
- Now, focus on the other number. In our example of 11,881,376, this would be the 81,376.

- Extracting Fifth Roots Mentally
- Look at just the rightmost digit. This will be the digit in the ones place of the answer!

- In our example of 11,881,376, we see that the rightmost digit is a 6. Therefore, the ones digit of the answer is also a 6!

- Extracting Fifth Roots Mentally
- Once you know both the tens digit and the ones digit of the answer, put them together and you have the fifth root.

- In our example, we determined that the answer for 11,881,376 is in the 20s, and that it ends in 6, so we give 26 as the fifth root!

- Extracting Fifth Roots Mentally
- Other examples:

- What is 5 147,008,443? Because 1470 is greater than 1,024 (4 5 ), and less than 3,125 (5 5 ), we know the answer is in the 40s. Because 08443 ends in 3, we know that the answer also ends in 3. Therefore, 5 147,008,443=43.

- Extracting Fifth Roots Mentally
- Other examples:

- What is 5 1,934,917,632? Because 19349 is greater than 16,807 (7 5 ), and less than 32,768 (8 5 ), we know the answer is in the 70s. Because 17632 ends in 2, we know that the answer also ends in 2. Therefore, 5 1,934,917,632=72.

- Extracting Fifth Roots Mentally
- Other examples:

- What is 5 8,587,340,257? Because 85,873 is greater than 59,049 (9 5 ), and less than 100,000 (10 5 ), we know the answer is in the 90s. Because 40257 ends in 7, we know that the answer also ends in 7. Therefore, 5 8,587,340,257=97.