Math Help - Surd q?

1. Surd q?

Rationalise the denominator of 1 + √3 ÷ (1 + √3)²

2. Originally Posted by Detanon
Rationalise the denominator and numerator of 1 + √3 ÷ (1 + √3)²
Multiply the denominator by its conjugate.

3. How do you find the conjugate?

4. Originally Posted by Detanon
How do you find the conjugate?
Example:

The conjugate of $a+b$ is $a-b$.

5. Originally Posted by Detanon
Rationalise the denominator of 1 + √3 ÷ (1 + √3)²
Hi Detanon,

The conjugate of $a+b\sqrt{r}$ is $a-b\sqrt{r}$

$\frac{1+\sqrt{3}}{(1+\sqrt{3})^2}=\frac{1+\sqrt{3} }{4+2\sqrt{3}}$

Now, multiply numerator and denominator by $4-2\sqrt{3}$

6. I got (1 + 2√3) ÷ 2. but in my book it says the answer is (5 + 3√3) ÷ 2

7. $\frac{1+\sqrt{3}}{(1+\sqrt{3})^2}=\frac{1+\sqrt{3} }{4+2\sqrt{3}}
$
$\times \frac{4-2\sqrt{3}}{4-2\sqrt{3}}=\frac{4-2\sqrt{3}+4\sqrt{3}-6}{16-12}=\frac{-2+2\sqrt{3}}{4}=\frac{-1+\sqrt{3}}{2}$