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Square roots review

Review square roots, and try some practice problems.

Square roots

The square root of a number is the factor that we can multiply by itself to get that number.
The symbol for square root is square root of, end square root .
Finding the square root of a number is the opposite of squaring a number.
Παράδειγμα:
start color #11accd, 4, end color #11accd, times, start color #11accd, 4, end color #11accd or start color #11accd, 4, end color #11accd, squared equals, start color #1fab54, 16, end color #1fab54
Έτσι square root of, start color #1fab54, 16, end color #1fab54, end square root, equals, start color #11accd, 4, end color #11accd
If the square root is a whole number, it is called a perfect square! In this example, start color #1fab54, 16, end color #1fab54 is a perfect square because its square root is a whole number.
Want to learn more about finding square roots? Check out this video.

Finding square roots

If we can't figure out what factor multiplied by itself will result in the given number, we can make a factor tree.
Παράδειγμα:
square root of, 36, end square root, equals, start text, question mark, end text
Here is the factor tree for 36:
So the prime factorization of 36 is 2, times, 2, times, 3, times, 3.
We're looking for square root of, 36, end square root, so we want to split the prime factors into two identical groups.
Notice that we can rearrange the factors like so:
36, equals, 2, times, 2, times, 3, times, 3, equals, left parenthesis, 2, times, 3, right parenthesis, times, left parenthesis, 2, times, 3, right parenthesis
So left parenthesis, 2, times, 3, right parenthesis, squared, equals, 6, squared, equals, 36.
So, square root of, 36, end square root is 6.

Εξάσκηση

Πρόβλημα 1
square root of, 64, end square root, equals, start text, question mark, end text
  • Η απάντησή σου έπρεπε να είναι
  • ενας ακέραιος, όπως το 6
  • ένα απλοποιημένο σωστο κλάσμα, όπως το 3, slash, 5
  • ένα απλοποιημένο καταχρηστικό κλάσμα, όπως το 7, slash, 4
  • ένας μεικτός αριθμός, όπως το 1, space, 3, slash, 4
  • ένας ακριβής δεκαδικός, όπως το 0, point, 75
  • ένα πολλαπλάσιο του π, όπως το 12, space, start text, p, i, end text ή το 2, slash, 3, space, start text, p, i, end text

Want to try more problems like this? Check out this exercise: Finding square roots
Or this challenge exercise: Equations with square and cube roots