Radical Calculator

A radical expression is of the form n√a, where:

• n is the index.
• a is the radicand.
• √ is the radical symbol.

To simplify a radical, we find the largest perfect n^th power that is a factor of the radicand. The process is as follows:

• Find the prime factorization of the radicand.
• Look for groups of prime factors that are the size of the index.
• For each group, move one factor from that group to the outside of the radical.
• Multiply the factors on the outside together.
• Multiply the remaining factors inside the radical together.

For example, to simplify √72, we find its prime factors: 2 × 2 × 2 × 3 × 3. We look for groups of 2 (the index). We find one group of 2's and one group of 3's. We move a 2 and a 3 outside, leaving a 2 inside. The result is (2 × 3)√2 = 6√2.