he crazy little function called square root! on the GRE

The symbol " " is referred as square root function or radical and the expression is referred as square root of . The square root of a number  is a number   such that . In other words,  is a number whose square is .

The symbol " " is referred as square root function or radical and the expression is referred as square root of .  Every positive number can potentially have two square roots. One of them is , which is positive, and the other is , which is negative.  However the square root function of a number always returns a non-negative number i.e. . 

Only the square root of a perfect square will be a rational number e.g. the square root of 16 is 4 because 16 is a perfect square. However the square root of 3 is not a rational number since 3 is not a perfect square i.e. 

You should memorize commonly used perfect squares outlined in the following table

Number
Perfect Square
Square Root Operation

The square root of a number can also be written in exponent form. The square root of a number is nothing but the number with an exponent of "1/2" e.g. the square root in  can also be written in exponent notation as 

Example:

Which of the following expressions represents the square root of 45?

A) 

B) 

C) 

D) 

E) 

Solution:

The number 45 can be written as 5 × 9. Therefore square root of 45 = 

= 

=