go step by step to reduce the radical
√240
Step 1: Find the prime factorization of 240.
240 can be factored into 2 * 2 * 2 * 2 * 3 * 5, or 2^4 * 3 * 5.
Step 2: Group the prime factors into pairs.
Pair up the 2's to get 2 * 2 * (2 * 2 * 3 * 5).
Step 3: Take the square root of each pair.
The square root of 2 * 2 is 2, so we can now write the expression as 2 * 2 * √(2 * 3 * 5 * 2).
Step 4: Multiply the remaining numbers together.
2 * 2 simplifies to 4, so we can write the expression as 4√(2 * 3 * 5 * 2).
Step 5: Simplify the expression.
2 * 2 * 5 is 20, so we can further simplify the expression to 4√(20 * 3).
20 can be factored into 2 * 2 * 5, so we can simplify it further to 4 * 2√(5 * 3).
Step 6: Simplify again.
2 * 3 is 6, so we can simplify the expression to 8√(5 * 6).
Therefore, the simplified form of √240 is 8√(5 * 6).