I need someone to check my homework answers. I don't really know this stuff but i'm trying to do better in math this year. I didn't understand how to do some either.

1. √12
I got 2√3

2. √9a^3
I got 3a

3. √8 * √2
I got 4

4.3√50
I got 15√2

5. √32
I got 4√2

6. √18a3 (all together)
I don't know how to do this one

7. 3√12b^2 (all together)
I got 6b√3

8. 4/√2
I got 2√2 (these confuse me the most)

9. √10/√2
I got √20/2

10. 2√3/2 (two square root three over two together)
I don't know how to do this one either

11. 3√3 - √27
Is it √3?

12. 2√50 + 3√32
I don't know how to do this one.

It would mean a lot if someone could help me. I'm not a bad student but i hate math. If i could understand it i could probably like it more.

In many of your questions, I can't tell how much is supposed to be under the �ã sign, so I cannot answer them with confidence.

The following are correct: 1,3,4,5,8
9: �ã10/�ã2 = �ã5*�ã2 /�ã2 = �ã5
10. 2 sqrt (3/2) = (2 /sqrt 2)*sqrt 3 = sqrt 2 * sqrt 3 = sqrt 6
11 No. It is 0
12. 2 sqrt 50 + 3 sqrt 32
= 2 sqrt (25*2) + 3 sqrt (16*2)
10 sqrt 2 + 12 sqrt 2 = 22 sqrt 2

I'd be happy to help you check your homework answers and understand how to solve these problems. Let's go through each question step by step:

1. √12
You correctly simplified the square root of 12 as 2√3. You can check this by multiplying 2√3 by itself: (2√3) * (2√3) = 4 * 3 = 12. Therefore, your answer is correct!

2. √9a^3
You simplified the square root of 9a^3 as 3a. However, this is not correct. To simplify this expression, you need to look for perfect squares within the square root. In this case, 9 is a perfect square because it is equal to 3^2. You can simplify it as follows: √9a^3 = √(3^2 * a^2 * a) = 3a√a. Therefore, the correct answer is 3a√a.

3. √8 * √2
To simplify this expression, you can multiply the two square roots together: √8 * √2 = √(8 * 2) = √16 = 4. Therefore, your answer is correct!

4. 3√50
You correctly simplified the cube root of 50 as 15√2. To check this, you can raise 15√2 to the power of 3: (15√2)^3 = 15^3 * (√2)^3 = 3375 * 2√2 = 6750√2. Therefore, your answer is correct!

5. √32
You simplified the square root of 32 as 4√2. You can check this by multiplying 4√2 by itself: (4√2) * (4√2) = 16 * 2 = 32. Therefore, your answer is correct!

6. √18a^3 (all together)
To simplify this expression, you can break it down into separate square roots: √(18a^3) = √(9 * 2 * a^2 * a) = 3a√(2a). Therefore, the correct answer is 3a√(2a).

7. 3√12b^2 (all together)
You correctly simplified the cube root of 12b^2 as 6b√3. To check this, you can raise 6b√3 to the power of 3: (6b√3)^3 = 6^3 * (b^2)^3 * (√3)^3 = 216 * b^6 * 3 = 648b^6√3. Therefore, your answer is correct!

8. 4/√2
To simplify this expression, you need to rationalize the denominator. To do this, you can multiply the expression by √2/√2 (which is just 1): (4/√2) * (√2/√2) = (4√2)/2 = 2√2. Therefore, the correct answer is 2√2.

9. √10/√2
To simplify this expression, you can rationalize the denominator in the same way as the previous question. Multiply the expression by (√2/√2): (√10/√2) * (√2/√2) = (√20)/2 = √20/2. Since √20 is not a perfect square, this expression cannot be simplified further. Therefore, your answer (√20/2) is correct.

10. 2√3/2 (two square root three over two together)
To simplify this expression, you can cancel out the common factor of 2 in the numerator and denominator: (2√3)/2 = √3. Therefore, the correct answer is √3.

11. 3√3 - √27
To simplify this expression, you need to find perfect squares within the square roots: 3√3 - √27 = 3√3 - √(3^3 * 3) = 3√3 - 3√3 = 0. Therefore, the correct answer is 0.

12. 2√50 + 3√32
To simplify this expression, you can factor out perfect squares from each square root: 2√50 + 3√32 = 2√(25 * 2) + 3√(16 * 2) = 2 * 5√2 + 3 * 4√2 = 10√2 + 12√2 = 22√2. Therefore, the correct answer is 22√2.

I hope this helps you understand how to simplify square roots and rationalize fractions in your math homework. If you have any more questions, feel free to ask!