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. Consider participating in the discussion by simplifying your classmates’ expressions. Detail what would have happened if the expression was not simplified first.
add sqrt 2 + sqrt 8
no way without first saying
sqrt 8 = sqrt (4*2) = 2 sqrt 2
then we have sqrt 2 + 2 sqrt 2 = 3 sqrt 2
It is important to simplify radical expressions before adding or subtracting because it helps to ensure that the expressions are in their simplest form. Simplifying radicals involves finding the square roots of perfect squares and combining like terms within the radical. This makes it easier to perform the operations and prevents mistakes in the calculations.
Adding radical expressions is similar to adding polynomial expressions because in both cases, you are combining similar terms. In polynomial expressions, you combine terms with the same variables and exponents by adding or subtracting the coefficients. Similarly, in radical expressions, you combine like radicals by adding or subtracting their coefficients.
However, adding radical expressions is different from adding polynomial expressions because radicals cannot be added directly if their radicands (the expression inside the radical) are not the same. To add or subtract radical expressions, the radicands have to be identical.
Here's a radical expression for you to simplify:
√12 + √27
To simplify this expression, you need to find the factors of each radicand and look for any factors that are perfect squares. Then, you can simplify the radicals by taking the square roots of the perfect squares:
√12 + √27 = √(4 * 3) + √(9 * 3)
= √4 * √3 + √9 * √3
= 2√3 + 3√3
= (2 + 3)√3
= 5√3
If the expression was not simplified first, you would have ended up with an incorrect result. For example, if you had directly added the radicals without simplifying, you would have obtained √12 + √27. This expression cannot be simplified further because 12 and 27 do not have any perfect square factors that can be extracted from them.