What is the difference between estimating a square root and simplifying a square root?
Example: The square root of 54
The square root of 54 is not an integer, since 54 is not a
perfect square. The square root of 54 will be between 7 and 8,
since 54 is between 49 and 64. Since 54 is closer to 49 than it is
to 64, the square root will be closer to 7 than 8. I'd estimate the
square root of 54 to be approximately 7.35
The actual square root is plus or minus 7.3484692
To simplify a square root, search for any factors greater than
one that are perfect squares. Since 54 = 9 x 6, the square root of
54 equals the square root of 9 x 6 equals the square root of 9
times the square root of 6. The square root of 9 is 3, so the
square root of 54 simplified is 3 times the square root of 6.