Roots

Things one must know:

• Odd roots will have the same sign as the base
• Even roots only have a positive value
• Break numbers into prime factors to find their roots
• Only roots linked by multiplication and division can be simplified
• Properties of roots (MGMAT NP p81)
• Squares and square roots to memorize (MGMAT NP p82)
• Simplifying a root: 1) factor the number under the radical sign into primes; 2) pull out any pair of matching primes from under the radical sign and place one of those pairs outside the root; 3) consolidate the expression
• Use the conjugate to rationalize the denominator of any fraction with a square root plus or minus another term, to find the conjugate, simply change the sign of the square root term.