Final answer:
The expression 2 √1.5√2 - 1.5√2 simplifies to 2 √3 - 1.5√2 when recognizing that 1.5√2 is a common term and combining like terms by subtraction.
Step-by-step explanation:
To simplify the expression 2 √1.5√2-1.5√2, first, we need to recognize that the radical sign √ indicates the square root of a number. Based on the given equation, we can associate the radical with a power of one-half, such that x² = √x. Applying this principle, we simplify the given expression by understanding that multiplying square roots is equivalent to taking the square root of the product of the numbers. In this case, the expression simplifies as follows:
- First, identify the terms involving square roots: 2 √(1.5 × 2) and 1.5√2.
- Observe that 1.5√2 is a common term in both parts of the expression.
- Since they are like terms, you can combine them by addition or subtraction. However, because the expression is 2 √1.5√2 - 1.5√2, you subtract the second term from the first.
- The subtraction leads to: 2 √3 - 1.5√2.
- Since there's no common term left after subtraction, this is as simplified as it can get without numeric approximation.
In this case, the simplification does not lead to a single number because the terms do not exactly cancel each other out or combine to form a simpler expression. Therefore, the simplified form of the expression is 2 √3 - 1.5√2.