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How Do You Find the Square Root of a Perfect Square?

What is the square root of 36?

Summary

  1. The definition of a square root starts out by defining 'a2=b'
  2. If 'a2=b', then the square root of 'b' equals 'a'!
  3. Since we know that 'b' is 36, let's try squaring some numbers to see if any of their squares equal 36
  4. 62 equals 36, so 'a' must be 6!

Notes

    1. 'a' and 'b' are variables here
    2. So if we know the value of 'a' or 'b', we can solve for the other variable!
    1. If we know the value of 'a' or 'b', we can solve for the other variable!
    2. In our given problem, 36 is equivalent to 'b' in our definition of a square root
    1. If we know the value of 'a' or 'b', we can solve for the other variable!
    2. In our given problem, 36 is equivalent to 'b' in our definition of a square root
    3. We can find the value for 'a' by going starting at 1 and squaring it
    1. If we know the value of 'a' or 'b', we can solve for the other variable!
    2. In our given problem, 36 is equivalent to 'b' in our definition of a square root
    3. We can find the value for 'a' by going starting at 1 and squaring it
    4. If 12 doesn't equal 36, then we'll keep 'guessing and checking'
    1. If we know the value of 'a' or 'b', we can solve for the other variable!
    2. In our given problem, 36 is equivalent to 'b' in our definition of a square root
    3. We can find the value for 'a' by going starting at 1 and squaring it
    4. 12 does NOT equal 36, so let's move on to 22 next
    1. If we know the value of 'a' or 'b', we can solve for the other variable!
    2. In our given problem, 36 is equivalent to 'b' in our definition of a square root
    3. 22 does NOT equal 36, so let's try 32 next
    1. If we know the value of 'a' or 'b', we can solve for the other variable!
    2. In our given problem, 36 is equivalent to 'b' in our definition of a square root
    3. '32' does NOT equal 36, nor does 42
    1. If we know the value of 'a' or 'b', we can solve for the other variable!
    2. In our given problem, 36 is equivalent to 'b' in our definition of a square root
    3. So far, 'a2' has equaled 1, 4, 9, and 16
    1. If we know the value of 'a' or 'b', we can solve for the other variable!
    2. In our given problem, 36 is equivalent to 'b' in our definition of a square root
    3. So far, 'a2' has equaled 1, 4, 9, and 16
    4. 52 does NOT equal 36, but again, we're getting closer to 36
    5. 62 DOES equal 36, so 'a' is 6!
    1. If we know the value of 'a' or 'b', we can solve for the other variable!
    2. In our given problem, 36 is equivalent to 'b' in our definition of a square root
    3. 62 equals 36, so 'a' is 6!
    1. If we know the value of 'a' or 'b', we can solve for the other variable!
    2. In our given problem, 36 is equivalent to 'b' in our definition of a square root
    3. 62 equals 36, so 'a' is 6, and the square root of 36 is 6!
    1. If we know the value of 'a' or 'b', we can solve for the other variable!
    2. In our given problem, 36 is equivalent to 'b' in our definition of a square root
    3. 62 equals 36, so 'a' is 6, and the square root of 36 is 6!