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 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 .
Since is , .
Find the square root.
indicates the negative square root of .
Since is , .
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 .
Observe that lies between the perfect squares and . That is, .
Now find the square root of each number.
So, is between and .
Since is much closer to than to , the best whole number estimate is .