The goal of simplifying radicals is to move as many whole numbers as possible from inside the square root to outside the square root. The way we do that is to build a prime factorization tree. When you have completed the tree, any like pairs of prime numbers are canceled out, and the prime gets put on the outside of the radical.
√48
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√2 √24
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√2 √12
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√2 √6
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√2 √3
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√2 √24
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√2 √12
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√2 √6
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√2 √3
There are two pairs of 2. Each pair gets to leave the radical (square root).
√2 x √2 = 2
√2 x √2 = 2
√2 x √2 = 2
√2 x √2 = 2
2 x 2 = 4
There is only one instance of the √3, so the 3 has to stay inside the square root, which means there is a 4 outside the radical, and a 3 inside.
4√3
Homework:
Study for quiz on simplifying radicals.
