# surds

• Oct 3rd 2009, 09:25 AM
surds
Can't fathom this one:

Express in the form a + b(root c)

(root 3 + root 2) (root 3 - root 2)

Thanks!
• Oct 3rd 2009, 09:28 AM
Quote:

Can't fathom this one:

Express in the form a + b(root c)

(root 3 + root 2) (root 3 - root 2)

Thanks!

HI

$(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})=(\sqrt{3})^2-(\sqrt{2})=1$

so when you express this in that form ..

a=1 , b and c are both 0 .
• Oct 3rd 2009, 09:46 AM
Quote:

HI

$(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})=(\sqrt{3})^2-(\sqrt{2})=1$

so when you express this in that form ..

a=1 , b and c are both 0 .

I get the 1, but thought the question was looking for integer values for b and c other than 0...because if b and c are 0, then you can't actually express as a + b root c?
• Oct 3rd 2009, 09:58 AM
e^(i*pi)
Quote:

I get the 1, but thought the question was looking for integer values for b and c other than 0...because if b and c are 0, then you can't actually express as a + b root c?

They can be zeroes, it still gives a real solution. The original question is multiplying a surd by it's conjugate which will always give a rational answer - it's how we rationalise the denominator.

You could say that $1 = 1+3\sqrt0$

As long as $bc = 0$ and $c \geq 0$ then it will work