it doesn't show you how to solve for a fraction.

for a fraction, you just find the roots for both the denominator and the numerator. For example, if you are finding the 4th root of 16/243, you find the 4th root of 16(which is 2) and the 4th root of 243(which is 3) so the answer would be 2/3. Hope that helped

What are imaginary numbers

It's a complex number that is written as i, which means the square root of -1, which is impossible.

I'm not getting this at all i need help

Try to [truly] understand what Sal is doing in this video: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:radicals/v/5th-roots

um so how come when i take a unit test its always something else instead of what i was taught...

i honestly think so to... but khan is trying to give you a challenge to expand your mind and DIY! thats why they make the tests harder!

How do you find a decimal root.

Do you mean the square root of a decimal such as √.64?

So tough but finally figured it out

Congratulations. Is this school required for you? If so, I feel your pain.😬

im a bit confused about the 9th root.

So basically they phrased the question in a tricky way. When they say: "Pick the correct equality that describes 2 as the ninth root of a number." You need to remember that the any root, whether higher order, cube, or square, is the inverse of its counterpart: exponents. So essentially the real question they are asking you is: 2 to the power 9. All you need to do is solve for this and your answer will coincide with one of the multiple choice.

If we can do square roots to cube roots to 5th roots to 7th roots then can we do 8th root, 9th root and 10th root etc?

Yep,any rational number can be a root and easily depicted

The basic logic behind roots is that you take the number and do the inverse of the exponents to arrive at your answer. For Example:- Solve. cube root of 343 if you have memorized the cube roots you know it is 7, but lets look at the algebraic steps to complete this question. 343 can be further divided to - 49 x 7 49 can be divided down to - 7 x 7 So, if you count up the '7's you see, you will see that there are three. So the answer would be 3. It's that easy! (unless if you don't get it, then I feel stupid saying that last part.)

Main content

Integrated math 1

Course: Integrated math 1 > Unit 13

Lesson 2: Radicals

Higher order roots

Google Classroom

In this article, we will expand the concepts of square roots and cube roots to roots of any order.

If you don't know what square and cube roots are, we recommend that you check out this lesson.

Quick review of square and cube roots

To find the square root of a number

x

, we look for a number whose square is

x

. For example, since

3^{2} = 9

, we say that the square root of

9

, written as

\sqrt{9}

, is

3

3^{2} = 9 ⟺ 3 = \sqrt{9}

Similarly, to find the cube root of a number

x

, we look for a number whose cube is

x

. For example, since

2^{3} = 8

, we say that the cube root of

8

, written as

\sqrt[3]{8}

, is

2

2^{3} = 8 ⟺ 2 = \sqrt[3]{8}

$4^{th}$ ‍ roots

Let's continue that pattern! To find the

4^{th}

root of a number

x

, we look for a number which, raised to the

4^{th}

power, equals

x

. For example, since

3^{4} = 81

, we say that the

4^{th}

root of

81

, written as

\sqrt[4]{81}

, is

3

3^{4} = 81 ⟺ 3 = \sqrt[4]{81}

Let's practice finding some $4^{th}$ ‍ roots

Problem 1.1

\sqrt[4]{16} =

$5^{th}$ ‍ roots

And our journey continues! To find the

5^{th}

root of a number

x

, we look for a number which, raised to the

5^{th}

power, equals

x

. For example, since

2^{5} = 32

, we say that the

5^{th}

root of

32

, written as

\sqrt[5]{32}

, is

2

2^{5} = 32 ⟺ 2 = \sqrt[5]{32}

Let's practice finding some $5^{th}$ ‍ roots

Problem 2.1

\sqrt[5]{243} =

Other higher order roots

We can continue this way and define

6^{th}

roots,

7^{th}

roots etc. For example,

3^{6} = 729

, so the

6^{th}

root of

729

, written as

\sqrt[6]{729}

, is

3

Let's do some more problems with higher order roots

Problem 3.1

\sqrt[7]{128} =

Want to join the conversation?

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Austin Dekruyf
Posted 4 years ago. Direct link to Austin Dekruyf's post “it doesn't show you how t...”
it doesn't show you how to solve for a fraction.
Button navigates to signup pageComment on Austin Dekruyf's post “it doesn't show you how t...”
(33 votes)
Answer
- cwang19
  Posted 4 years ago. Direct link to cwang19's post “for a fraction, you just ...”
  for a fraction, you just find the roots for both the denominator and the numerator. For example, if you are finding the 4th root of 16/243, you find the 4th root of 16(which is 2) and the 4th root of 243(which is 3) so the answer would be 2/3.
  Hope that helped
  Comment on cwang19's post “for a fraction, you just ...”
  (87 votes)
d.williams
Posted 4 years ago. Direct link to d.williams's post “What are imaginary number...”
What are imaginary numbers
Button navigates to signup pageComment on d.williams's post “What are imaginary number...”
(25 votes)
Answer
- HYENA
  Posted 4 years ago. Direct link to HYENA's post “It's a complex number tha...”
  It's a complex number that is written as i, which means the square root of -1, which is impossible.
  Comment on HYENA's post “It's a complex number tha...”
  (38 votes)
Junior Small
Posted 4 years ago. Direct link to Junior Small's post “I'm not getting this at a...”
I'm not getting this at all i need help
Button navigates to signup pageComment on Junior Small's post “I'm not getting this at a...”
(20 votes)
Answer
- Strange Quark
  Posted 3 years ago. Direct link to Strange Quark's post “Try to [truly] understand...”
  Try to [truly] understand what Sal is doing in this video: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:radicals/v/5th-roots
  Button navigates to signup page
  (9 votes)
Khynedi Hubbard
Posted 4 years ago. Direct link to Khynedi Hubbard's post “um so how come when i tak...”
um so how come when i take a unit test its always something else instead of what i was taught...
Button navigates to signup pageComment on Khynedi Hubbard's post “um so how come when i tak...”
(16 votes)
Answer
- 𝘽𝘼𝙏𝙈𝘼𝙉
  Posted 4 years ago. Direct link to 𝘽𝘼𝙏𝙈𝘼𝙉's post “i honestly think so to......”
  i honestly think so to... but khan is trying to give you a challenge to expand your mind and DIY! thats why they make the tests harder!
  Comment on 𝘽𝘼𝙏𝙈𝘼𝙉's post “i honestly think so to......”
  (22 votes)
Emmanuelle Hounguevou
Posted 4 years ago. Direct link to Emmanuelle Hounguevou's post “How do you find a decimal...”
How do you find a decimal root.
Button navigates to signup pageComment on Emmanuelle Hounguevou's post “How do you find a decimal...”
(9 votes)
Answer
- David Severin
  Posted 4 years ago. Direct link to David Severin's post “Do you mean the square ro...”
  Do you mean the square root of a decimal such as √.64?
  Comment on David Severin's post “Do you mean the square ro...”
  (16 votes)
Faridah Be
Posted 4 years ago. Direct link to Faridah Be's post “im a bit confused about t...”
im a bit confused about the 9th root.
Button navigates to signup pageComment on Faridah Be's post “im a bit confused about t...”
(7 votes)
Answer
- Spriha Dharan
  Posted 3 years ago. Direct link to Spriha Dharan's post “So basically they phrased...”
  So basically they phrased the question in a tricky way. When they say: "Pick the correct equality that describes 2 as the ninth root of a number." You need to remember that the any root, whether higher order, cube, or square, is the inverse of its counterpart: exponents. So essentially the real question they are asking you is: 2 to the power 9. All you need to do is solve for this and your answer will coincide with one of the multiple choice.
  Button navigates to signup page
  (13 votes)
Quinton Brett
Posted 4 years ago. Direct link to Quinton Brett's post “So tough but finally figu...”
So tough but finally figured it out
Button navigates to signup pageComment on Quinton Brett's post “So tough but finally figu...”
(9 votes)
Answer
- 🏅🎖️
  Posted 4 years ago. Direct link to 🏅🎖️'s post “Congratulations. Is this ...”
  Congratulations. Is this school required for you? If so, I feel your pain.😬
  Comment on 🏅🎖️'s post “Congratulations. Is this ...”
  (7 votes)
taylorkokesh
Posted 7 months ago. Direct link to taylorkokesh's post “how do you do this?”
how do you do this?
Button navigates to signup pageComment on taylorkokesh's post “how do you do this?”
(3 votes)
Answer
- Rishik C
  Posted 6 months ago. Direct link to Rishik C's post “The basic logic behind ro...”
  The basic logic behind roots is that you take the number and do the inverse of the exponents to arrive at your answer.
  
  For Example:-
  
  Solve.
  
  cube root of 343
  
  if you have memorized the cube roots you know it is 7, but lets look at the algebraic steps to complete this question.
  
  343 can be further divided to - 49 x 7
  
  49 can be divided down to - 7 x 7
  
  So, if you count up the '7's you see, you will see that there are three.
  
  So the answer would be 3.
  
  It's that easy!
  
  (unless if you don't get it, then I feel stupid saying that last part.)
  Comment on Rishik C's post “The basic logic behind ro...”
  (17 votes)
Rohan Soni
Posted 3 years ago. Direct link to Rohan Soni's post “If we can do square roots...”
If we can do square roots to cube roots to 5th roots to 7th roots then can we do 8th root, 9th root and 10th root etc?
Button navigates to signup pageComment on Rohan Soni's post “If we can do square roots...”
(6 votes)
Answer
- loumast17
  Posted 3 years ago. Direct link to loumast17's post “Yep,any rational number c...”
  Yep,any rational number can be a root and easily depicted
  Comment on loumast17's post “Yep,any rational number c...”
  (7 votes)
Genesis Morales
Posted 3 years ago. Direct link to Genesis Morales's post “Is there a easier way to ...”
Is there a easier way to find a higher roots answer
Button navigates to signup pageButton navigates to signup page
(8 votes)
Answer
- aquila-chrysaetos
  Posted 9 months ago. Direct link to aquila-chrysaetos's post “Other than using a calcul...”
  Other than using a calculator, I don't think so.
  Comment on aquila-chrysaetos's post “Other than using a calcul...”
  (0 votes)

Integrated math 1

Course: Integrated math 1 > Unit 13

Quick review of square and cube roots

4th‍ roots

Let's practice finding some 4th‍ roots

5th‍ roots

Let's practice finding some 5th‍ roots

Other higher order roots

Let's do some more problems with higher order roots

Want to join the conversation?

$4^{th}$ ‍ roots

Let's practice finding some $4^{th}$ ‍ roots

$5^{th}$ ‍ roots

Let's practice finding some $5^{th}$ ‍ roots