Algebra and logic: Proceedings Clayton, 1974 by Crossley J.N. (ed.)

By Crossley J.N. (ed.)

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You are left with: ^72 = 2 X 3 X -J l = 6V2 . M M ANHATTAN GMAT Roots Chapter 4 Memorize: Squares and Square Roots You should memorize the following squares and square roots, as they often appear on the GMAT. 25 22 = 4 74=2 32 = 9 79 = 3 42= 16 Vl6 = 4 52 = 25 y[25=5 62 = 36 436=6 ii 12= 1 749=7 82 = 64 764=8 92 = 81 •781= 9 102 = 100 V io o l l 2 = 121 7121=11 122 = 144 7l44=12 132 = 169 •7l69 =13 142 = 196 Vl96 = 14 152 = 225 •7225 =15 162 = 256 7256 =16 202= 400 740 0= 20 252 = 625 7625 = 25 302= 900 7900 = 30 = 10 MANHATTAN GMAT 55 Chapter 4 Roots Memorize: Cubes and Cube Roots You should memorize the following cubes and cube roots, as they often appear on the GMAT.

0° is undefined. That’s because — is undefined. Negative Exponents The behavior of negative exponents is also an extension of the rules for dividing exponential terms. / / _ yxy yXyXyXyXy _ i y3 Look at this division by subtracting exponents: y Therefore, y 3 = —r. This is the general rule: something with a negative exponent is just “one over” that same thing with a positive exponent. This rule holds true even if the negative exponent appears in the denominator, or if the negative expo­ nent applies to a fraction.

If (z + 3 )2 = 25, w hat is z? You could solve this problem by distributing the left-hand side of the equation, setting the right-hand side equal to zero, and factoring. However, it would be much easier to simply take the square root of both sides of the equation to solve for z. You just have to consider both the positive and the negative square root. yj(z + 3 )2 = V25 Note that square-rooting the square of something is the same as taking the absolute value of that thing. \z+3\ = 5 z + 3 = ±5 z = -3 ± 5 z = { 2 , - 8} Going in Reverse: Use FOiL__________________ Instead of starting with a quadratic equation and factoring it, you may need to start with factors and rewrite them as a quadratic equation.

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