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

Why is it important to simplify radical expressions before adding or subtracting?

You have to simplify radical expressions before adding or subtracting because you can only add or subtract expressions with the same value inside the radical sign.
How is adding radical expressions similar to adding polynomial expressions? How is it different?
It is similar to adding polynomials because in polynomials you can also only add or subtract terms if they are like terms (variables with the same powers). In radical expressions, you can also only add or subtract like terms (the same value inside the radical). One main difference is that in polynomials, like terms are determined by the variables and their powers, while in radical expressions, like terms are determined by the value inside the root.
Provide a radical expression for your classmates to simplify.
Consider participating in the discussion by simplifying your classmates' expressions. Detail what would have happened or if the expression was not simplified first.
Here is an example for the classmates:
sqrt(180) - sqrt(20)
Factor the 180 and 20:
sqrt(5*36) - sqrt(5*4)
Simplify:
6 * sqrt(5) - 2 * sqrt(5)
Subtract:
4 * sqrt(5)
If you did not simplify this expression first, you would end up with the wrong answer.

answer this problemSQRT (18) + SQRT (72).

It is important to simplify radical expressions before adding or subtracting them because it allows for clearer and more manageable calculations. Simplifying a radical expression involves finding the numerical value of the square root, cube root, or higher root, and combining like terms if possible. This simplification helps in reducing the complexity of the expression and makes it easier to perform addition or subtraction operations.

Adding radical expressions is similar to adding polynomial expressions in that both involve combining similar terms to create a simplified expression. In both cases, like terms are grouped together and coefficients are added or subtracted accordingly.

However, adding radical expressions is different from adding polynomial expressions because radical terms often cannot be combined directly. In order to combine radical expressions, the terms must have the same radicand (the quantity underneath the radical symbol) and the same index (the number indicating the root). If the terms do not have the same radicand and index, they cannot be simplified further.

Here is a radical expression for your classmates to simplify: √12 + √27.

It is important to simplify radical expressions before adding or subtracting because it helps to avoid errors and obtain the most simplified form possible. Simplifying radicals involves rewriting them in the simplest form by removing any perfect square factors from the radicand (the number inside the radical symbol) and minimizing the use of radicals.

Adding radical expressions is similar to adding polynomial expressions because both involve combining like terms. In both cases, you look for similar terms and combine coefficients or radicals together.

However, adding radical expressions is different from adding polynomial expressions because radical expressions involve the square root or other roots of numbers, while polynomial expressions consist of variables raised to whole number exponents. The presence of radicals adds complexity and requires additional steps to perform the addition or subtraction.

Here is a radical expression for simplification:
√(18x^2) + 3√(2x)

To simplify this expression, we start by finding any perfect square factors in the radicand:
√(18x^2) = √(9 * 2 * x^2) = 3√(2x^2)

Now, we have:
3√(2x) + 3√(2x)

Since both terms have the same radical, we can combine them:
3√(2x) + 3√(2x) = 6√(2x)

Thus, the simplified form of the given radical expression is 6√(2x).