Give an example and explain one or more of the following: How do we add, subtract, multiply OR divide with radicals?
Example:
Let's say we want to add two radical expressions: √5 + √2.
To add these radicals, we first check if the radicands (the numbers inside the square roots) are the same. In this case, the radicands are 5 and 2, which are different.
So, we cannot directly combine them. However, we can simplify the expression by finding the simplest radical form for each of the radicands.
√5 cannot be simplified further because 5 is a prime number.
√2 can be simplified by finding the largest perfect square that divides evenly into 2, which is 1. So we can write √2 as √(1*2).
Now, let's rewrite our original expression with the simplified radical forms:
√5 + √2 = √5 + √(1*2) = √5 + √(1)√(2) = √5 + √2.
Since the radicands are different, we cannot combine these radicals any further. So our final answer is √5 + √2.
Note: The same process applies for subtraction and multiplication of radicals, but division is slightly different. In division, we simplify the radicands and then divide them. For example, √9 ÷ √3 = (√(3*3)) ÷ √3 = 3 ÷ √3 = 3/√3 = (3/√3) ∙ (√3/√3) = (3√3)/3 = √3.
can u make thats smaller
Sure! Here's a shorter explanation:
When adding radical expressions, we first check if the radicands are the same. If they are, we can simply add or subtract the coefficients. If the radicands are different, we simplify each radicand as much as possible and then combine.
To simplify a radicand, we identify the largest perfect square factor. For example, to simplify √8, we find that 4 is the largest perfect square that divides evenly into 8. So, √8 becomes 2√2.
For multiplication of radicals, we can directly multiply the coefficients and the radicands.
For division of radicals, we simplify the radicands and then divide them.
Remember, always simplify the radicands as much as possible to get the simplest form.