Explanation:
To simplify the expression √3 * √5 * √12, you can combine the square roots and simplify the numbers under the radicals.
Step 1: Simplify the numbers under the radicals:
√3 = √(3) (The square root of 3 cannot be simplified further because 3 is a prime number.)
√5 = √(5) (The square root of 5 cannot be simplified further because 5 is a prime number.)
√12 = √(4 * 3) (The number 12 can be expressed as the product of 4 and 3, and the square root of 4 simplifies to 2.)
√12 = 2√(3)
Step 2: Combine the simplified square roots:
√3 * √5 * √12 = √(3) * √(5) * 2√(3)
Step 3: Apply the rule of multiplying square roots:
√(3) * √(5) = √(3 * 5) = √15
Step 4: Substitute the simplified square roots back into the expression:
√3 * √5 * √12 = √15 * 2√(3)
Step 5: Simplify the expression further:
√15 * 2√(3) = 2√(15) * √(3) = 2√(15 * 3) = 2√(45)
Step 6: Simplify the number under the square root:
2√(45) = 2√(9 * 5) = 2√(9) * √(5) = 2 * 3 * √(5) = 6√(5)
Therefore, the simplified form of √3 * √5 * √12 is 6√5.