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!

So tough but finally figured it out

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

How do you find a decimal root.

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

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.

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

Get ready for Algebra 2

Course: Get ready for Algebra 2 > Unit 4

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, squared, equals, 9, we say that the square root of 9, written as square root of, 9, end square root, is 3.

3, squared, equals, 9, \Longleftrightarrow, 3, equals, square root of, 9, end square root

Similarly, to find the cube root of a number x, we look for a number whose cube is x. For example, since 2, cubed, equals, 8, we say that the cube root of 8, written as cube root of, 8, end cube root, is 2.

2, cubed, equals, 8, \Longleftrightarrow, 2, equals, cube root of, 8, end cube root

4, start superscript, start text, t, h, end text, end superscript roots

Let's continue that pattern! To find the 4, start superscript, start text, t, h, end text, end superscript root of a number x, we look for a number which, raised to the 4, start superscript, start text, t, h, end text, end superscript power, equals x. For example, since 3, start superscript, 4, end superscript, equals, 81, we say that the 4, start superscript, start text, t, h, end text, end superscript root of 81, written as root, start index, 4, end index, is 3.

3, start superscript, 4, end superscript, equals, 81, \Longleftrightarrow, 3, equals, root, start index, 4, end index

Let's practice finding some 4, start superscript, start text, t, h, end text, end superscript roots

Problem 1.1

Current

root, start index, 4, end index, equals

5, start superscript, start text, t, h, end text, end superscript roots

And our journey continues! To find the 5, start superscript, start text, t, h, end text, end superscript root of a number x, we look for a number which, raised to the 5, start superscript, start text, t, h, end text, end superscript power, equals x. For example, since 2, start superscript, 5, end superscript, equals, 32, we say that the 5, start superscript, start text, t, h, end text, end superscript root of 32, written as root, start index, 5, end index, is 2.

2, start superscript, 5, end superscript, equals, 32, \Longleftrightarrow, 2, equals, root, start index, 5, end index

Let's practice finding some 5, start superscript, start text, t, h, end text, end superscript roots

Problem 2.1

Current

root, start index, 5, end index, equals

Other higher order roots

We can continue this way and define 6, start superscript, start text, t, h, end text, end superscript roots, 7, start superscript, start text, t, h, end text, end superscript roots etc. For example, 3, start superscript, 6, end superscript, equals, 729, so the 6, start superscript, start text, t, h, end text, end superscript root of 729, written as root, start index, 6, end index, is 3.

Let's do some more problems with higher order roots

Problem 3.1

Current

root, start index, 7, end index, equals

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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...”
(32 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 ...”
  (71 votes)
d.williams
Posted 4 years ago. Direct link to d.williams's post “What are imaginary number...”
What are imaginary numbers
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(24 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...”
  (37 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...
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(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......”
  (20 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.
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(9 votes)
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- 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...”
  (15 votes)
ElliotP
Posted 5 months ago. Direct link to ElliotP's post “who is in a classroom rn”
who is in a classroom rn
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(16 votes)
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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.
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(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 3 years ago. Direct link to Quinton Brett's post “So tough but finally figu...”
So tough but finally figured it out
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(10 votes)
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- 🏅🎖️
  Posted 3 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)
miss.d.ects
Posted a year ago. Direct link to miss.d.ects's post “I wish we could add scree...”
I wish we could add screenshots so we could get help with problems that are not on Khan.
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taylorkokesh
Posted 5 months ago. Direct link to taylorkokesh's post “how do you do this?”
how do you do this?
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(3 votes)
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- Rishik C
  Posted 3 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)