What is the process we follow when adding and subtracting radical expressions? Explain the process and demonstrate with an example.
I'll give you a list steps to follow:
1. Determine the lowest common denominator (LCD) for the rational numbers.
2. Express each rational number as an equivalent rational number with the LCD as the denominator.
3. Combine the rational numbers by adding/subtracting numerators.
4. Reduce to lowest terms.
Example.
3x/4 + x/5
The LCD for both fractions is 20. For the first fraction you times both numerator and denominator by 5 to get 15x/20. And for the second fraction, you times x and 5 by 4 to get 4x/20. Then you just add across the numerators. Which gives you 19x/20.
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= 15�ã3 + 6�ã3 - 16�ã3
= 5�ã3 Someone help me understand this process please??
When adding or subtracting radical expressions, the general process involves simplifying the radicals, if possible, and then combining like terms.
Here are the step-by-step guidelines to follow:
1. Simplify each radical expression: Simplify the radicals individually by finding perfect square factors inside the square roots and moving them outside. Also, simplify any whole numbers under the radicals.
2. Identify like terms: Look for radical expressions with the same radicand and the same index (square root, cube root, etc.). These are considered like terms.
3. Combine like terms: Add or subtract the coefficients of the like terms while keeping the radicand and the index the same.
Now, let's demonstrate the process with an example:
Example: Simplify and add the radical expressions: √6 + 3√2 - 2√6 + 5√2
Step 1: Simplify each radical expression:
- For √6, there are no perfect square factors inside, so it remains as √6.
- For 3√2, there are no perfect square factors inside, so it remains as 3√2.
- For -2√6, there are no perfect square factors inside, so it remains as -2√6.
- For 5√2, there are no perfect square factors inside, so it remains as 5√2.
Step 2: Identify like terms:
- There are two like terms with a radicand of 6: √6 and -2√6.
- There are two like terms with a radicand of 2: 3√2 and 5√2.
Step 3: Combine like terms:
- The like terms with a radicand of 6 are √6 and -2√6. Combining their coefficients, we get: √6 - 2√6 = -√6.
- The like terms with a radicand of 2 are 3√2 and 5√2. Combining their coefficients, we get: 3√2 + 5√2 = 8√2.
Therefore, the simplified expression is: -√6 + 8√2.
When adding or subtracting radical expressions, it is important to simplify the expressions involved and combine any like terms. Here is a step-by-step process to follow:
1. Simplify the radicals: If possible, simplify each radical expression by simplifying the square roots. Look for perfect squares within the radicals and simplify them.
2. Identify the like terms: Look for radicals that have the same radicand (the number inside the square root symbol) and the same index (the small number in the upper left corner of the square root symbol). These are considered like terms and can be combined.
3. Combine like terms: Add or subtract the coefficients (the numbers in front of the square root symbols) of the like terms.
4. Simplify: If necessary, simplify the resulting expression further by repeating steps 1 to 3, until no further simplification is possible.
Let's demonstrate with an example:
Consider the expressions √12 - 2√3 + 3√12 + 4√3
Step 1: Simplify the radicals
√12 can be simplified as 2√3 because 3 is the largest perfect square factor of 12.
Similarly, √12 in the second term can also be simplified as 2√3.
So, the expression becomes 2√3 - 2√3 + 3√12 + 4√3
Step 2: Identify the like terms
We have two pairs of like terms: 2√3 and -2√3, and 3√12 and 4√3.
Step 3: Combine like terms
Combine the coefficients of the like terms:
(2 - 2)√3 + 3√12 + 4√3
Simplify further:
0√3 + 3√12 + 4√3
Step 4: Simplify
Since 0 multiplied by anything is 0, we can eliminate the first term:
3√12 + 4√3
Now, we can't simplify any further because there are no more like terms.
So, the final simplified expression is 3√12 + 4√3.