How do you subtract radicals?
Example wise.
Lets say you have sqrt16-sqrt8. sqrt8=2sqrt2 and sqrt16=4sqrt2 so the answer is 2sqr2, or sqrt8. Or, you could have sqrt27-sqrt3. sqrt27=3sqrt3, so it is 3sqrt3-sqrt3=2sqrt3=sqrt12.
Got it! thank you.
To subtract radicals, you need to follow these steps:
Step 1: Simplify each radical individually if possible.
- If there are perfect square factors inside the radicals, simplify them.
- For example: √12 = √(4 * 3) = 2√3
Step 2: Check if the radicals have the same index (root). If they do, proceed to the next step. If not, you cannot directly subtract them.
Step 3: Subtract the numbers outside the radicals (coefficients) and write them in front of the result.
Step 4: Subtract the numbers inside the radicals.
- If the numbers inside the radicals are the same, subtract them directly.
- For example: 5√3 - 3√3 = 2√3
- If the numbers inside the radicals are different, you cannot directly subtract them. In such cases, you can only simplify or combine them further if possible.
Here's an example to illustrate the process:
Question:
Simplify: √32 - √8
Step 1: Simplify each radical individually:
√32 = √(16 * 2) = 4√2
√8 = √(4 * 2) = 2√2
Step 2: Both radicals have the same root (√2), so we can subtract them.
Step 3: Subtract the coefficients in front of the radicals:
4√2 - 2√2 = 2√2
Therefore, √32 - √8 = 2√2.