Simplifying Square Roots
A square root of a number is one of two equal factors of the number. A radical sign, 
, is used to indicate a positive square root.
Every positive number has a positive square root and a negative square root. A negative number like –4 has no real square root because the square of a number cannot be negative.
Example:
Find the square root.
indicates the positive square root of 49.
Since 7 × 7 is 49, = 7.
Find the square root.
indicates the negative square root of 25.
Since 5 × 5 is 25, = –5 .
Estimate Square Root
The square root of a perfect square is an integer. You can estimate the square root of a number that is not a perfect square.
Example:
Estimate 
to the nearest whole number.
First list some perfect squares and look for the whole numbers near by 69.
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, …
Observe that 69 lies between the perfect squares 64 and 81. That is, 64 < 69 < 81.
Now find the square root of each number. 
So, is between 8 and 9.
