Question

What is the following quotient 1/1+ sqrt 3

Answer 1

Let us rewrite the given expression:

$\frac{1}{1+\sqrt{3}}$

Now in this case we have to rationalise the denominator.

So we multiply and divide by 1 - √3

$\frac{1}{1+\sqrt{3}}*\frac{1-\sqrt{3}}{1-\sqrt{3}}$

The denominator can be simplified using the property:

$(a+b)(a-b)=a^{2}-b^{2}$

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

So finally on simplifying we will get:

$\frac{1-\sqrt{3}}{-2}$

Answer 2

Answer:The following quotient of:

$\frac{1}{1+\sqrt{3}}=\frac{\sqrt{3}-1}{2}$

Step-by-step explanation:

$\frac{1}{1+\sqrt{3}}$

multiply and divide by $1-\sqrt{3}$

$\frac{1}{1+\sqrt{3}}\times \frac{1-\sqrt{3}}{1-\sqrt{3}}$

Using identity $(a+b)(a-b)=a^2-b^2$

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

$\frac{1-\sqrt{3}}{-2}=\frac{\sqrt{3}-1}{2}$

The following quotient of:

$\frac{1}{1+\sqrt{3}}=\frac{\sqrt{3}-1}{2}$