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What Happens When You Square a Square Root?

How do you square a square root?

Summary

  1. 'b' is a variable that can stand for any number
  2. The √ symbol going over the 'b' is the symbol for square root
  3. Squaring a number just means taking it to the 2nd power
  4. Squaring and taking the square root are opposites, so they undo each other
  5. So when you square a square root, your answer will be the number under the square root
  6. The square root of 36 is 6
  7. The square root of 25 is 5

Notes

    1. Just like addition and subtraction are opposite operations, squaring and taking the square roots are also opposites
    1. 'b' is just a variable, it could stand for any number
    2. Squaring a number means we're raising it to the 2nd power
    3. Since squaring and taking the square root are opposites, they undo each other
    1. 'b' is just a variable, it could stand for any number
    1. So we'll be raising the square root of 36 to the 2nd power
    1. Remember √36 means the square root of 36!
    1. 6•6 is 36, so the square root of 36 is 6
    2. In other words, √36=6
    1. So when we squared the square root of 36, we just ended up with 36
    1. Remember √25 means the square root of 25!
    1. 5•5 is 25, so the square root of 25 is 5
    2. In other words, √25=5
    1. 52, or 5•5, is 25
    1. Again we end up with 25, which was the number originally under our square root symbol
    1. This works with any number, no matter what is under the square root
    1. 'a' and 'b' are just variables here, they can stand for any number
    2. Using algebra you would write this by saying if a2=b then √b = a
    1. 'a' and 'b' are just variables here, they can stand for any number
    1. 'a' and 'b' are just variables here, they can stand for any number
    1. 'a' and 'b' are just variables here, they can stand for any number
    2. Since a2=b, we can substitute b for a2 into our equation
    1. 'a' and 'b' are just variables here, they can stand for any number
    2. Since a2=b, we can substitute b for a2 into our equation
    1. 'b' is just a variable, it could stand for any number
    1. 'a' and 'b' are just variables here, they can stand for any number
    2. Since a2=b, we can substitute b for a2 into our equation
    1. 'b' is just a variable, it could stand for any number
    2. This is what we were trying to prove!