the question is:
What is the sum of 5 radical 7 and 3 radical 8?
i don't understand how to solve this because i cant pull out a perfect square
5√7 + 3√8
stays that way, since we cannot add/subtract radicals with different bases (radicands)
but its a multiple choice and it doesnt have that as one of the choices...
you could simplify the last term to
6√2 but you still couldn't add them
do they have 5√7 + 6√2 ?
To solve the problem, we can simplify each radical separately and then combine them. Here's how to do it step by step:
1. Start with the sum of 5√7 and 3√8.
2. Simplify √7:
- Since 7 is not a perfect square, we cannot simplify it any further.
- So, we leave 5√7 as it is.
3. Simplify √8:
- Find the largest perfect square that divides 8, which is 4.
- √8 can be rewritten as √(4 × 2).
- Using the properties of radicals, we can split this into two terms: √4 × √2.
- Since √4 is 2, the simplified form is 2√2.
4. Now that we have simplified both radicals, we can add them together:
- 5√7 + 3√8 = 5√7 + 3(2√2).
- Distribute the 3 to each term: 5√7 + 6√2.
5. We cannot further simplify 5√7 and 6√2 because they involve different radicals.
So, the sum of 5√7 and 3√8 is 5√7 + 6√2.
Note: It's important to understand that radical expressions cannot be simplified by simply pulling out perfect squares. In this case, we had to split the square root of 8 into square root of 4 times square root of 2 and simplify it further.