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Square roots of perfect squares

Learn how to find the square root of perfect squares like 25, 36, and 81.
Let's start by taking a look at an example evaluating the square root of start color #1fab54, 25, end color #1fab54:
square root of, start color #1fab54, 25, end color #1fab54, end square root, equals, question mark
Step 1: Ask, "What number squared equals start color #1fab54, 25, end color #1fab54?"
Step 2: Notice that start color #11accd, 5, end color #11accd squared equals start color #1fab54, 25, end color #1fab54.
start color #11accd, 5, end color #11accd, squared, equals, start color #11accd, 5, end color #11accd, times, start color #11accd, 5, end color #11accd, equals, start color #1fab54, 25, end color #1fab54
The answer
square root of, start color #1fab54, 25, end color #1fab54, end square root, equals, start color #11accd, 5, end color #11accd
Here's a question to make sure you understood:
How can we be sure that start color #11accd, 5, end color #11accd is the right answer?
Choose 1 answer:
Choose 1 answer:

Connection to a square

Finding the square root of start color #1fab54, 25, end color #1fab54 is the same as finding the side length of a square with an area of start color #1fab54, 25, end color #1fab54.
A square with an area of start color #1fab54, 25, end color #1fab54 has a side length of start color #11accd, 5, end color #11accd.

Practice Set 1:

Problem 1A
4, squared, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Reflection question

Which claim shows how square roots work?
Choose 1 answer:
Choose 1 answer:

Practice Set 2:

Problem 2A
square root of, 1, end square root, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Practice Set 3:

Problem 3A
square root of, 121, end square root, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Want to join the conversation?

  • duskpin tree style avatar for user ELLEN
    is this 8th-grade math?
    im in 5th grade:+
    (5 votes)
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  • female robot ada style avatar for user aniza white
    How can we use square roots in life?
    (6 votes)
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  • starky sapling style avatar for user Gigi💙
    Would you do the same for a negative square root ?🤔
    (2 votes)
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    • leaf orange style avatar for user Benny C
      You cannot find the negative square root of a number. Think of what square roots are. If we take 36 and find the square root, you'll see it's 6. Because 6 x 6 = 36. We multiply it by itself and it gives us 36.

      We can't do this with negatives. Consider -36 and finding the square root of that. Which number multiplied by itself will get -36?

      Well, remember the rules we have for multiplying negatives and positives.
      negative x negative = positive
      negative x positive = positive
      positive x positive = positive.

      It can't be -6, because that will give us a positive number, instead of -36.
      It can't be 6, because that will also give us a positive number instead of -36.

      So, negatives can't have square roots.

      You'll learn in more advanced classes what we do in these cases.
      (8 votes)
  • primosaur tree style avatar for user osagier430
    can a decimal have a square root
    (4 votes)
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  • piceratops ultimate style avatar for user FoxLegend
    How to calculate imperfect squares?
    (3 votes)
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    • mr pants pink style avatar for user Autumn
      imperfect square roots (example: 32 SQUARE)(I am going to do square uppercased because I don't know how to make a square root sign)
      32 SQUARE
      start with the number you think is closest to this number
      25 SQUARE
      than the other closest
      36 SQUARE
      than just find the root of these numbers
      5
      6
      it is between 5 and 6
      hope this helped and may God bless your day
      (5 votes)
  • leaf red style avatar for user Gavin1027
    If I take a times table and I start to go across down I'll get the square roots right?
    1,4,9,16,25,36...
    (4 votes)
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  • starky tree style avatar for user ah5425
    How do you estimate square roots?
    (3 votes)
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    • starky tree style avatar for user echoi
      Using the exponent of whole numbers, you can estimate square roots.
      For example, √39 is a little bigger than 6 squared, which is 36, and it is smaller than 7 squared, which is 49. We can estimate √39 to be between 6 and 7, a little closer to 6.
      Hope this helped you.
      (2 votes)
  • hopper cool style avatar for user Artemis
    How do we know if the answer is positive of negative? e.g. 9 = 3^2 or 9 = -3^2. Are both answers acceptable?
    (2 votes)
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    • primosaur tree style avatar for user Bradley Reynolds
      Many times you will see something like this √9 = ±3. The "±" is pronounced "plus or minus" and you will see it in things like quadratic formula. But, sometimes both answers are NOT acceptable. For example, if you are using the pythagorean theorem and trying to get a side length, a negative answer won't work (you cannot have a negative side length). Other scenarios in which you can determine is when you simply know what sign the answer is supposed to be in.
      (3 votes)
  • boggle yellow style avatar for user Macy L.
    Is there an equation to find the square root of a number? (Ex: Evaluate the square root of 81; I know that it's 9, but would there be a way to find out if it was a larger number that I didn't know the answer to?)
    (3 votes)
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  • aqualine ultimate style avatar for user kaihla.leithauseryoung
    can a negative become a positive by an exponent?
    (2 votes)
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    • mr pink green style avatar for user David Severin
      Not quite the right question, but in multiplying (and thus exponents) the number of negatives determines the sign of the answer, so even number of negatives (or even exponents) gives positive answer, negative number (odd exponents give negative answer)
      So (-2)^2=4 (-2)^3=-8 (-2)^4=16, (-2)^5=-32
      (3 votes)