A Guide to the GRE/Radicals

Radicals can be multiplied and divided, and perfect squares can be extracted.

A radical is a number which equals another number if multiplied by itself a given number of times. The most common type of radical is the square root. Square roots can be multiplied and divided, as indicated above, but they cannot be added or subtracted.does not necessarily equal , but does equal

It is generally frowned upon placing a radical in the denominator of a fraction. To remove a radical from the denominator, multiply both the numerator and the denominator by the radical. For example,

In these problems, solve for x.

1.

2.

3.

1.

Take the initial equation.

Multiply both sides by

Divide both sides by 3.

2. y = 3

Take the initial equation.

Square both sides.

Work out the parentheses.

Subtract 5 from both sides.

3.

Take the initial equation.

Multiply both sides by

Divide both sides by 7.