Root (or radical)
The opposite of an exponent (in a sense). √16 means: what number (or numbers), when multiplied by itself twice, will yield 16? In this case, both 4 and -4 would multiply to 16 mathematically. However, when the GMAT provides the square root sign for an even root, such as a square root, then the only accepted answer is the positive root, 4. That is, √16 = 4, NOT +4 or -4. In contrast, the equation x^2 = 16 has TWO solutions, +4 and -4.
Even Root
A root using an even number, such as a square root or a fourth root. Even roots have only a positive value on the GMAT.
Odd Root
A root using an odd number, such as a cube root or a fifth root. Odd roots will have the same sign as the base of the root. For example, CBRT(64) = 4, CBRT(-27) = -3.
Simplifying Roots
Roots can be combined or split apart if the operation between the terms is multiplication or division. √(4 * 9) = √4 * √9.
Note:
If the operation between the terms is addition or subtraction, you cannot separate or combine the roots! √(4 + 9) DOES NOT EQUAL √4 + √9.
Perfect Square Roots
Perfect square roots will yield an integer. √25 = 5.
Imperfect Square Roots
Imperfect square roots do not yield an integer. √30 is not an integer, but it is between √25 and √36, or between 5 and 6.
Conjugate
For (a + √b), the conjugate is (a - √b). For (a - √b), the conjugate is (a + √b).
