Simplifying Radicals

by Chance Lopez

Important Terms

radical sign: indicates the root of a number

radicand: the number inside the radical sign

prime numbers: any number that can't be divided into a whole number

factor tree: breaking down a number into just its primes

Simplifying Square Roots

First, you're going to simplify 72 into 9 and 8. 9 gets simplified into 3 and 3 and since 3 is a prime number, circle them so you know they can't be simplified any more. Simplify 8 into 2 and 4 and circle 2 since it's a prime number. But since 4 isn't a prime number simplify it into 2 and 2 and circle them. After you simplify 72 into all prime numbers, you're going to put all of the circled numbers inside the radical sign. Since there is a pair of twos and a pair of threes, you bring out of the radical sign and leave the remainder 2 inside the radical sign. multiply the 3 and the 2 to get 6 and you have your answer of 6 times the square root of 2.
Simplifying Square Roots

Simplifying Cube Roots

Like finding the square root of a number, you need to do the same when finding the cube root of a number, create a factor tree. Simplify 135 into 5 and 27, circle 5. Simplify 27 into 3 and 9, circle 3. Simplify 9 into 3 and 3 and circle them. Put all of the circled numbers into the radical sign. This time instead looking for pairs of numbers you'll look for numbers in three. So since there are three threes, it will come out and you'll have the answer of 3 times the cube root of 5.
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