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Question

Please help me with the following problems. If you answer all of them accuratly, i will give you best answer.

1. 6 root (3) (root (11) + root (3) (sorry I can't type the square root sign so root and then the number following it just means the square root of that number in the parenthesis)

2. (2 root (2) + 5)(2 root (2) -5)

3. (9 root (3) + 6 root (2))(2 root (3) + 6 root (2))

4. x+10= 10 root (x + 5)

5. root (6) times root (3)-5 root (50)

6. root (5a) + 6 root (45a) + 5 root (125a)

Answer 1

I'll do a couple as examples, to get you started:

2.) (2√2 + 5)(2√2 - 5)
Step 1: Factor it out:
2√2 * 2√2 + 5 * 2√2 - 5 * 2√2 - 25

Step 2: Break it into pieces:
2√2 * 2√2 = 2 * 2 * √2 * √2 = 4 * 2 = 8
5 * 2√2 - 5 * 2√2 = 0

Step 3: Add it up.
8 + 0 - 25 = -13.

3.) (9√3 + 6√2)(2√3 + 6√2)
Same as #2.
Step 1: Factor out.
9√3 * 2√3 + 6√2 * 2√3 + 9√3 * 6√2 + 6√2 * 6√2

Step 2: Break it down.
9√3 * 2√3 = 9 * 2 * √3 * √3 = 18 * 3 = 56
6√2 * 2√3 = 6 * 2 * √2 * √3 = 12 * √6 = 12√6
9√3 * 6√2 = 9 * 6 * √3 * √2 = 54 * √6 = 54√6
6√2 * 6√2 = 6 * 6 * √2 * √2 = 36 * 2 = 72

Step 3: Add it up.
56 + 72 + 12√6 + 54√6 = 128 + 66√6

For multiplication, you treat the numbers outside and inside the root seperately, so 2√2 * 2√2 = (2 * 2)*(√2 * √2).
For addition, you can't add dissimilar roots: √2 + √3 can't be combined. You can add similar roots, however: 2√2 + √2 = 3√2.

Answer 2

Dan,

You need to make a trip to see your math instructor. You have a lot of different types of problems here.