Why is it important to simplify radical expressions before adding or subtracting? How is adding radical expressions similar to and different from adding polynomial expressions? Provide a radical expression for your classmates to simplify.


In your own words, explain the first condition that must be met for a simplified radical. Explain why 5/(sqrt(2)) is not simplified and demonstrate the steps we must take to simplify it.

Review section 10.2 (p. 692) of your text. How do the laws work with rational exponents? Provide the class with an expression to simplify that includes rational (fractional) exponents.

explain the first condition that must be met for a simplified radical.

It is important to simplify radical expressions before adding or subtracting because it allows us to work with smaller, more manageable numbers and reduces the chances of making mistakes during computations. Simplifying radical expressions involves finding the perfect square factors of the numbers under the radicals and simplifying them as much as possible.

Adding radical expressions is similar to adding polynomial expressions in that we combine like terms. However, adding radical expressions also involves simplifying the radicals before adding. This is different from adding polynomial expressions, where we simply combine the coefficients of like terms.

To simplify a radical expression, let's consider the expression 3√(18x^2). The first condition for a simplified radical is that there are no perfect square factors remaining inside the radical. In this case, we can simplify the expression by finding the perfect square factors of 18, which are 9 and 2. We can rewrite √(18x^2) as √(9x^2) * √(2). Since √(9x^2) simplifies to 3x, we get 3x√2 as the simplified radical expression.

Now, let's take a look at the expression 5/(√2). This expression is not simplified because the denominator contains a radical. To simplify it, we multiply the numerator and denominator by the conjugate of the denominator, which in this case is √2. By doing this, we get (5 * √2) / (√2 * √2). Simplifying further, we get (5√2) / 2 as the simplified radical expression.

In terms of rational exponents, the laws work similarly to integer exponents. One important law is the power of a product rule, which states that (ab)^n = a^n * b^n. This means that we can distribute the exponent to each factor in the expression.

Here's an expression to simplify that includes rational exponents: (∛x^2)^2. To simplify this, we can apply the power of a product rule. First, simplify (∛x^2) to x^(2/3), and then raise it to the second power. Applying the power of a product rule, we get x^(2/3 * 2) = x^(4/3) as the simplified expression.