Thread: hopefully a quick surd question

1. hopefully a quick surd question

ok this question hopefully will not take long, I do not understand this question at all.

Express 3+2√75/
3-√12

in the form a+b√3 where a,b e(the symbol meaning is a member of in replace of the e) R\{0}

2. Ok to do this

first off please be more careful with how you denote things...I am assuming your question is simplify $\frac{3+2(75)^{\frac{1}{2}}}{3-(12)^{\frac{1}{2}}}$if so what you must first do is simplfiy the radicals since $(75)^{\frac{1}{2}}=(3*5^2)^{\frac{1}{2}}$ you can rewrite it as $5(3)^{\frac{1}{2}}$ and using the same method $(12)^{\frac{1}{2}}=2(3)^{\frac{1}{2}}$ so this whole thing is equal to $\frac{3+10(3)^{\frac{1}{2}}}{3-2(3)^{\frac{1}{2}}}$ now I am sure you can go from there...ill tell you the answer its $-12(3)^{\frac{1}{2}}-23$

3. Mathstud- yes it is right, it looks different to what I thought it would be nontheless is works so many thanks for your help.

4. ah, now ive just stumbled upon another insane surd question. This one is much easier to read.

(√a+√b)²=a+b+2√ab

determine the square root of 17+6√8

I hope you can help,
thanks.

5. Originally Posted by glenn101
ah, now ive just stumbled upon another insane surd question. This one is much easier to read.

(√a+√b)²=a+b+2√ab

determine the square root of 17+6√8

I hope you can help,
thanks.