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 18.1 Know Your Numbers 18.2 Order of Operations 18.3 Odd and Even Numbers 18.4 The Positive, the Negative, and the Ugly 18.5 Divisibility and Remainders 18.6 Factors 18.7 Multiples 18.8 Know Your Fractions

 18.9 Decimals 18.10 Percents 18.11 Ratios 18.12 Exponents 18.13 Roots and Radicals 18.14 Sequences 18.15 Sets
Here’s what you already know: (1) roots express fractional exponents; (2) it’s often easier to work with roots by converting them into expressions that look like this:
Roots and powers are reciprocals. To square the number 3, multiply 3 by itself: 32 = 3 3 = 9. To get the root of 9, , you have to find the number that, multiplied by itself, will equal 9. That number is 3.
Square roots appear far more often than any other kind of root on the SAT, but cube roots, fourth roots, fifth roots, and so on could conceivably make an appearance. Each root is represented by a radical sign with the appropriate number next to it (a radical without any superscript denotes a square root). For example, cube roots are shown as , fourth roots as , and so on. Roots of higher degree operate the same way square roots do. Because 33 = 27, it follows that the cube root of 27 is 3.
Here are a few examples: