radicals....can someone please help?

Question

Please help with all you can. Thanks

1. √100a^4b^2c^2

2. (√x-√y)^2

3. 12√15-9√75+8√45-6√225

4. √x^5/y^2

5. √24/16

sorry this was supposed to be under mathematics.

Answer 1

This is not the sort of radical with which one normally deals in Chemistry...

1. √(100a^4b^2c^2)
= √100 √a^4 √b^2 √c^2
= 10a^2|bc|. (If b and c are positive then this is just 10a^2bc, which is probably the answer your teacher will give you.)

2. (√x - √y)^2 = (√x)^2 - 2(√x)(√y) + (√y)^2
= x - 2√(xy) + y.

3. 12√15 - 9√75 + 8√45 - 6√225
= √15 (12 - 9√5 + 8√3 - 6√15)
= √15 [3 (4 - 3√5) + (2√3) (4 - 3√5)]
= √15 (3 + 2√3) (4 - 3√5).

4. √(x^5/y^2) = √(x^4) √x / √ y^2
= x^2√x / |y|.

5. √(24/16) = √(3/2)
Not much more you can do with that one. If you mean (√24) / 16 then you get 2√6 / 16 = √6 / 8 = √3 / 4√2.