How to simplify square roots (review) (article) | Khan Academy (2024)

Learn how to rewrite square roots (and expressions containing them) so there's no perfect square within the square root. For example, rewrite√75 as 5⋅√3.

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  • skilavera1

    5 years agoPosted 5 years ago. Direct link to skilavera1's post “what grade maths would th...”

    what grade maths would this be?

    (17 votes)

    • Beaniebopbunyip

      5 years agoPosted 5 years ago. Direct link to Beaniebopbunyip's post “I think it’s about eighth...”

      How to simplify square roots (review) (article) | Khan Academy (4)

      How to simplify square roots (review) (article) | Khan Academy (5)

      How to simplify square roots (review) (article) | Khan Academy (6)

      I think it’s about eighth or ninth grade. But people take math at different times. I’ve known fith graders who have taken algebra and geometry in the same year, and I’ve known ninth graders who have taken algebra. Even if you’re taking algebra in ninth grade, that’s okay. What really matters is that you understand the content when you learn it.

      (68 votes)

  • Jaidyn McPherson

    6 years agoPosted 6 years ago. Direct link to Jaidyn McPherson's post “when will we ever use thi...”

    when will we ever use this in everyday life? whats the point of even learning this?

    (15 votes)

    • AD Baker

      5 years agoPosted 5 years ago. Direct link to AD Baker's post “Jaidyn, After learning ...”

      Jaidyn,

      After learning this helps you pass your Math class and graduate high school, there are many careers where this is used. Most obviously, it's used in engineering and computer science. However, when I worked in construction, I used to use square roots regularly to determine whether items would fit through a doorway on a diagonal. (Note: this also involves trigonometry.)

      (53 votes)

  • dylan.forr99

    a year agoPosted a year ago. Direct link to dylan.forr99's post “Anyone else need to take ...”

    Anyone else need to take like 4 or 5 hours to really get a firm understanding of this lesson? or am I just dumb?

    (17 votes)

    • Gina

      a year agoPosted a year ago. Direct link to Gina's post “Sometimes things snap rig...”

      Sometimes things snap right into place and the light goes on right away, and other times we need review and practice. If you got this far, you already have all the pieces you need to work with radicals. It's a matter of seeing how they go together.

      (7 votes)

  • Ha

    6 years agoPosted 6 years ago. Direct link to Ha's post “can a fraction be an expo...”

    can a fraction be an exponent?

    (10 votes)

    • Redapple8787

      6 years agoPosted 6 years ago. Direct link to Redapple8787's post “A fraction can be an expo...”

      How to simplify square roots (review) (article) | Khan Academy (19)

      A fraction can be an exponent. When a fraction is an exponent, you can change it so that a there is a first, second, third, etc. root of something.
      For example,
      1^1/2 = square root of 1
      1^1/3 = third root of 1
      1^1/4 = fourth root of 1
      And so on and so forth. This was covered in a series of videos in the topic Rational Exponents and Radicals.
      https://www.khanacademy.org/math/algebra/rational-exponents-and-radicals/alg1-rational-exp-eval/v/fractional-exponents-with-numerators-other-than-1

      (15 votes)

  • bjacobsen4427

    a year agoPosted a year ago. Direct link to bjacobsen4427's post “golly gracious i think iv...”

    golly gracious i think ive passed out 15 times trying to these

    (19 votes)

  • Lateo

    8 years agoPosted 8 years ago. Direct link to Lateo's post “In the video "Simplifying...”

    In the video "Simplifying square roots (variables)" @

    How to simplify square roots (review) (article) | Khan Academy (23) 1:40

    Sal explains "as I said in the last video, the principal root of X squared is going to be the absolute value of X, just in case X is a negative number". I have two questions:
    (1) Can anybody please point me to that video? I can't find it.
    (2) I don't understand the need for an absolute value. If we state, before beginning to solve the problem, that the domain of the X variable is the Positive Real Numbers (or X greater than or equal to zero), aren't we already cancelling out the possibility that the X variable assumes a negative value by restricting the domain, thus rendering the use of the absolute value unnecessary?

    (11 votes)

  • will.lindner.student

    6 years agoPosted 6 years ago. Direct link to will.lindner.student's post “what about problems with ...”

    what about problems with a number already multiplying the square root. Do you multiply or add the numbers together?

    (5 votes)

    • David Lee

      6 years agoPosted 6 years ago. Direct link to David Lee's post “It's easier to understand...”

      It's easier to understand if there is an example. Let's say you have √98. 98 is 49*2 which is 7^2*2, it would be 7√2. If you have 2√98. √98 is 7√2, 2√98 would be 14√2.

      Hope this helps! If you have any questions or need help, please ask! :)

      (9 votes)

  • Misheel

    3 years agoPosted 3 years ago. Direct link to Misheel's post “Can i also simplify √72 ...”

    Can i also simplify √72 in this way: √72 = √9*8 = √9*√8 = 3√8

    instead of: √72 = √2*36 = √36*√2 = 6√2

    (3 votes)

    • Kim Seidel

      3 years agoPosted 3 years ago. Direct link to Kim Seidel's post “Yes, you can take that ap...”

      How to simplify square roots (review) (article) | Khan Academy (31)

      Yes, you can take that approach. But, your work is incomplete. When you simplify a square root, you need to ensure you have removed all perfect squares. With 3√8, you still have a perfect square inside the radical.
      3√8 = 3√(4*2) = 3√4 * √2 = 3*2√2 = 6√2
      Hope this helps.

      (12 votes)

  • daniel wauchope

    4 years agoPosted 4 years ago. Direct link to daniel wauchope's post “how do you do long divisi...”

    how do you do long division

    (0 votes)

    • jonahfish

      4 years agoPosted 4 years ago. Direct link to jonahfish's post “let me show you an exampl...”

      How to simplify square roots (review) (article) | Khan Academy (35)

      let me show you an example: 129/3

       43 three "goes in" 43 times
      ______
      3|129
      12 3 goes into 12 four times
      -12 minus 3*4 (in between 12 and 0, and 3,0 there is a line)
      09 remainder of 0. bring down the 9
      3

      (17 votes)

  • kjohnson8937

    3 years agoPosted 3 years ago. Direct link to kjohnson8937's post “how would we solve x!=120”

    how would we solve x!=120

    (5 votes)

    • David Severin

      3 years agoPosted 3 years ago. Direct link to David Severin's post “Factorials are based on m...”

      Factorials are based on multiplying all numbers below the number, so start dividing out starting at 2 until you reach the number you want. So 120/2=60/3=20/4=5. Answer is 5!.

      (6 votes)

How to simplify square roots (review) (article) | Khan Academy (2024)

FAQs

How do you simplify square root answers? ›

Step 1: Find the prime factors of the number inside the radical sign. Step 2: Group the factors into pairs. Step 3: Pull out one integer outside the radical sign for each pair. Leave the other integers that could not be paired inside the radical sign.

How do you memorize square roots easily? ›

Step 1: Pair the digits from right to left, 404 01. Step 2: Check the unit digit of the number and compare it with the above table. Here, the unit digit is 1, thus possible unit digits for the square root of 40401 is 1 and 9. But the square root of 1 is 1, thus unit digit will have 1.

How to solve square root step by step? ›

Long division method
  1. Separate your square root base into pairs. ...
  2. Find the largest square that divides into the first number or pair. ...
  3. Subtract the square from the first number or pair. ...
  4. Drop down the next pair. ...
  5. Multiply the first digit of the square by two. ...
  6. Set up the next factor equation.

What grade is simplifying square roots? ›

IXL | Simplify square roots | 8th grade math.

Which method is best for square root? ›

If the number is a perfect square, such as 4, 9, 16, etc., then we can factorize the number by prime factorisation method. If the number is an imperfect square, such as 2, 3, 5, etc., then we have to use a long division method to find the root.

Can you simplify the square root? ›

Simplifying a square root isn't as hard as it looks. To simplify a square root, you just have to factor the number and pull the roots of any perfect squares you find out of the radical sign.

How to simplify square roots variables? ›

Simplifying square roots with variables is similar to simplifying square roots without variables. Treat the variable as a factor--if it appears twice (x [ 2 ] ), cross out both and write the factor (x) one time to the left of the square root sign.

How do you solve square roots step by step? ›

Here are the steps to the long division method:
  1. Separate your square root base into pairs. ...
  2. Find the largest square that divides into the first number or pair. ...
  3. Subtract the square from the first number or pair. ...
  4. Drop down the next pair. ...
  5. Multiply the first digit of the square by two. ...
  6. Set up the next factor equation.
Aug 8, 2022

How to tell if a square root can be simplified? ›

You can simplify a radical if it has a factor of the appropriate power — sticking with square roots for the time being, you can simplify a square root if it has a square factor. √50, for example, is √(2 x 5 x 5), so you can rewrite that as 5√2.

How to simplify the square root of 145? ›

sqrt(145) No simplification exists, Root remains : • sqrt(145) Simplify : sqrt(145) Factor 145 into its prime factors 145 = 5 • 29 To simplify a square root, we extract ...

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