How do you rationalize and divide $\frac{2 + \sqrt{3}}{2 - \sqrt{3}}$ $(2+sqrt3) /(2-sqrt3)$ ?

Question

How do you rationalize and divide $\frac{2 + \sqrt{3}}{2 - \sqrt{3}}$ $(2+sqrt3) /(2-sqrt3)$ ?

1 Answer

Impact of this question

1373 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-04-03T21:55:55

Using the identity $(a + b) (a - b) = a^{2} - b^{2}$ $(a+b)(a-b)=a^2 - b^2$ , let's multiply and divide the fraction by $2 + \sqrt{3}$ $2+\sqrt{3}$ . You'll notice that, when doing so, at the numerator you'll have ${(2 + \sqrt{3})}^{2}$ $(2+\sqrt{3})^2$ , while at the denominator you'll have $(2 - \sqrt{3}) (2 + \sqrt{3})$ $(2-\sqrt{3})(2+\sqrt{3})$ , which is the formula mentioned at the beginning.

So, $(2 - \sqrt{3}) (2 + \sqrt{3}) = 2^{2} - {(\sqrt{3})}^{2} = 4 - 3 = 1$ $(2-\sqrt{3})(2+\sqrt{3})=2^2 - (\sqrt(3))^2 = 4-3=1$ .

Since the denominator is $1$ $1$ , we can ignore it, and the final answer is thus ${(2 + \sqrt{3})}^{2}$ $(2+\sqrt{3})^2$

Science

Math

Humanities

... and beyond

How do you rationalize and divide $\frac{2 + \sqrt{3}}{2 - \sqrt{3}}$ $(2+sqrt3) /(2-sqrt3)$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you rationalize and divide 2+√32−√3(2+sqrt3) /(2-sqrt3)?

1 Answer

Related questions

Impact of this question

How do you rationalize and divide $\frac{2 + \sqrt{3}}{2 - \sqrt{3}}$ $(2+sqrt3) /(2-sqrt3)$ ?