What is the process we follow when multiplying and dividing radical expressions? Explain the process and demonstrate with an example
I think I already explained this to you down below.
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= x�ã3 - �ã18 Multiplying radicals
3�ãy(3�ãy3 + 3�ã3) = 3�ãy * 3�ãy3 + 3�ãy * 3�ã3 Using a distributive law
= 3�ãy3 + 3�ã2y Multiplying radicals
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I don't know what font you have, but the symbols come out all garbled. try using √ for root and repost.
When multiplying and dividing radical expressions, we follow certain steps to simplify the expressions. Let's break down the process:
1. Simplify each radical expression: The first step is to simplify each radical expression individually. This involves finding perfect square factors of the radicand (the number under the radical) and taking them out of the radical.
2. Multiply or divide the coefficients: After simplifying the radicands, we then multiply or divide the coefficients (numbers outside the radicals) as usual. Keep in mind that if there is no coefficient explicitly shown, it is considered to be 1.
3. Combine the like terms: Finally, combine any like terms by adding or subtracting them based on the operation (multiplication or division) being performed.
Let's demonstrate these steps with an example:
Example: Simplify and evaluate the expression (2√6)(√2/√3).
Step 1: Simplify each radical expression:
- For 2√6, we can break it down as (√2)(√3).
- For √2, there are no perfect square factors, so it remains the same.
- For √3, there are no perfect square factors either.
Now we have (2√6)(√2/√3) = (√2)(√3)(√2/√3).
Step 2: Multiply the coefficients:
- The coefficient of the first radical expression is 2.
- The coefficient of the second radical expression is 1 (implicitly).
Now we have (2)(1)(√2/√3) = 2√2/√3.
Step 3: Combine like terms:
- There are no like terms to combine in this example.
So the simplified expression is 2√2/√3.
It's important to note that sometimes we might need to rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator. However, in this example, the denominator is already rationalized.
Remember to always simplify each radical expression, perform the arithmetic operations on the coefficients, and combine like terms to solve problems involving multiplying or dividing radical expressions.