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.
Example:
start color blueD, 4, end color blueD, times, start color blueD, 4, end color blueD or start color blueD, 4, end color blueD, start superscript, 2, end superscript equals, start color greenD, 16, end color greenD
So square root of, start color greenD, 16, end color greenD, end square root, equals, start color blueD, 4, end color blueD
If the square root is a whole number, it is called a perfect square! In this example, start color greenD, 16, end color greenD 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.
Example:
square root of, 36, end square root, equals, question mark
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, start superscript, 2, end superscript, equals, 6, start superscript, 2, end superscript, equals, 36.
So, square root of, 36, end square root is 6.

Practice

Problem 1
square root of, 64, end square root, equals, question mark
  • 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, p, i or 2, slash, 3, space, p, i

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