simplify
7*3^1/2-5*2^1/2/(48^1/2-18^1/2)
To simplify the given expression, we need to follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).
Let's break down the expression step by step:
1. Start with the numerator of the expression: 7 * 3^(1/2) - 5 * 2^(1/2).
- The exponent 1/2 means taking the square root of a number.
- 3^(1/2) equals the square root of 3, which is approximately 1.732.
- Similarly, 2^(1/2) equals the square root of 2, which is approximately 1.414.
2. Therefore, the numerator becomes 7 * 1.732 - 5 * 1.414.
Moving on to the denominator of the expression:
3. Evaluate the square roots of the numbers in the denominator: 48^(1/2) - 18^(1/2).
- The square root of 48 is approximately 6.928.
- The square root of 18 is approximately 4.243.
4. Now, we can rewrite the expression with the simplified values:
numerator = 7 * 1.732 - 5 * 1.414
denominator = 6.928 - 4.243.
5. Perform the multiplication and subtraction in the numerator and the denominator separately:
numerator = 12.124 - 7.070
denominator = 2.685.
6. Finally, divide the numerator by the denominator:
numerator / denominator = 12.124 - 7.070 / 2.685.
So, the simplified value of the given expression is approximately 4.51.