4. 3�ã11 + 4�ã11 Answer: 8�ã11

7. 7�ã2 - 2�ã8 Answer: 1�ã2 ??
8. �ã48 + �ã75 Answer: 9�ã3
9.(3�ã10) Answer: 19 + 6�ã10
10. �ã27/64 (Fractions) Answer 3�ã3/8 ??
11. 10�ã20 - 3�ã80 Answer: 10�ã5
12. �ã6/49 Fractions) Answer: �ã6/7 ??
13. 3�ã2 * �ã14 Answer:stays the same ??
14. �ã6/50 Answer: 10�ã3
15. �ã30 * 2�ã12 Answer: �ã30 * 4�ã3

If I got any of these wrong, can someone please tell me how to do them correctly?

I will assume your ã means 'square root'

4. 3�ã11 + 4�ã11 Answer: 8�ã11 --- I recall 3+4 used to be 7, not 8

7. 7�ã2 - 2�ã8 Answer: 1�ã2 ??

---- 7√2 - 2(2√2) = 3√2

9.(3�ã10) Answer: 19 + 6�ã10 --- how did you get that ????
---- 3√10 stays that way

11. 10�ã20 - 3�ã80 Answer: 10�ã5 --- NO

10(√4)(√5) - 3(√16)(√5) = 20√5 - 12√5 = 8√5

13. 3�ã2 * �ã14 Answer:stays the same ?? --- no

----- 3√2 * √14 = 3√28 = 3(√4)(√7) = 6√7

14. �ã6/50 Answer: 10�ã3 --- not clear, is the 50 part of the square root ?
If so, then √(6/50) = √(3/25) = (√3)/5
If it is (√6)/50 then it stays that way

15. �ã30 * 2�ã12 Answer: �ã30 * 4�ã3 -- don't understand what you did

√30 * 2√12 = 2√360 = 2(√9)(√4)(√10) = 24√10

Here's an explanation for each of the problems:

4. To add 3√11 and 4√11, you can combine the coefficients (numbers in front of the radical) and keep the same radical term. So, 3√11 + 4√11 = (3 + 4)√11 = 7√11. Therefore, the correct answer is 7√11.

7. To subtract 2√8 from 7√2, you can do the same as addition. Combine the coefficients and keep the same radical term. So, 7√2 - 2√8 = (7 - 2)√2 = 5√2. Therefore, the correct answer is 5√2.

8. To add √48 and √75, you can simplify the radicals and then combine them. √48 can be simplified as 4√3, and √75 can be simplified as 5√3. Then, you can combine the coefficients and keep the same radical term. So, √48 + √75 = 4√3 + 5√3 = (4 + 5)√3 = 9√3. Therefore, the correct answer is 9√3.

9. To simplify √(3√10), you can think of it as raising the inner radical to the exponent of 1/2. So, √(3√10) = (10^(1/2))(3^(1/2)) = √10 * √3 = √(10 * 3) = √30. Therefore, the correct answer is √30.

10. To simplify √(27/64), you need to simplify the numerator and the denominator separately. √27 can be simplified as 3√3, and √64 can be simplified as 8. Then, you can divide the simplified numerator by the simplified denominator. So, √(27/64) = (3√3)/8. Therefore, the correct answer is (3√3)/8.

11. To subtract 3√80 from 10√20, you can simplify the radicals and then subtract them. √80 can be simplified as 4√5, and √20 can be simplified as 2√5. Then, you can subtract the simplified radicands and keep the same radical term. So, 10√20 - 3√80 = 10√5 - 3√5 = (10 - 3)√5 = 7√5. Therefore, the correct answer is 7√5.

12. To simplify √(6/49), you need to simplify the numerator and the denominator separately. √6 cannot be simplified any further, and √49 is equal to 7. Then, you can divide the simplified numerator by the simplified denominator. So, √(6/49) = √6/7. Therefore, the correct answer is √6/7.

13. When you multiply 3√2 by √14, you can simply multiply the coefficients and the radicands separately. So, 3√2 * √14 = 3 * 14 * √(2 * 1) = 42 * √2. Therefore, the correct answer stays the same, which is 42√2.

14. To simplify √(6/50), you need to simplify the numerator and the denominator separately. √6 cannot be simplified any further, and √50 can be simplified as 5√2. Then, you can divide the simplified numerator by the simplified denominator. So, √(6/50) = √6/5√2 = √6/(5 * √2) = √6/(5√2) * (√2/√2) = (√6 * √2)/(5 * √2 * √2) = (√12)/(5 * 2) = (√12)/10. Therefore, the correct answer is (√12)/10.

15. When you multiply √30 by 2√12, you can multiply the coefficients and the radicands separately. So, √30 * 2√12 = 2 * 30 * √(12 * 1) = 60 * √12. Therefore, the correct answer is 60√12.

I've reviewed your answers and made corrections where necessary.