Surd q?

**Detanon** · December 17th 2009, 05:12 AM

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

**VonNemo19** · December 17th 2009, 05:14 AM

Originally Posted by Detanon

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

Multiply the denominator by its conjugate.

**Detanon** · December 17th 2009, 05:57 AM

How do you find the conjugate?

**VonNemo19** · December 17th 2009, 06:04 AM

Originally Posted by Detanon

How do you find the conjugate?

Example:

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

**masters** · December 17th 2009, 06:12 AM

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 $4-2\sqrt{3}$

**Detanon** · December 17th 2009, 07:00 AM

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

**dedust** · December 17th 2009, 07:11 AM

$\frac{1+\sqrt{3}}{(1+\sqrt{3})^2}=\frac{1+\sqrt{3} }{4+2\sqrt{3}}<br />$ $\times \frac{4-2\sqrt{3}}{4-2\sqrt{3}}=\frac{4-2\sqrt{3}+4\sqrt{3}-6}{16-12}=\frac{-2+2\sqrt{3}}{4}=\frac{-1+\sqrt{3}}{2}$

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