Will the sum or difference of two radical expressions always yield a radical expression? Will the product or quotient of two radical expressions always yield a radical expression? Explain.
Since a negative number times a negative number is always a positive number, it si important to remember taking a square root that the answer will be both a positive and a negative number or expression. It is important to be careful about those situations.
We can consider some radical expressions and then should be simplified to be solved. At times, when we simplify them, they may change to a non- radical expression, at the time of taking product or dividing two radical expressions. We can only add or subtract two radical expressions if the radicands are the same. On the other hand, sometimes the radicands might seem different, but it’s possible to simplify them and get the same radicand as a result. Thus, we can subtract two radical expressions. In the case of addition and subtraction, the result will be a radical expression itself.
The sum or difference of two radical expressions will be the result of these radical expressions either added or subtracted. Meaning if we have square root 2 plus square root 3, this will not be equal to square root of 5, but instead it will be the result of square root 2 plus the result of square root 3. Whereas the product of the same numbers will be the same as if we multiplied those numbers under the square root. So radical 2 times radical 3 will be the same as radical 6.