Question

Rationalize the denominator root 3 minus 1 divided by root 3 plus 1

Answer 1

Answer:

$2 - \sqrt{3}$

Step-by-step explanation:

ATQ,

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

When we say to rationalize the denominator, we mean that the numerator and denominator have to be multiplied by a number such that the denominator becomes a rational number. Here in this case, we multiply it with

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

Then we can use the following algebraic identity to simplify it

$(x + y)(x - y) = {x}^{2} - {y}^{2}$

Where,

$x = \sqrt{3} \\ y = 1$

So,

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

Hence the answer

Answer 2

Answer:

2-√3 is the correct answer.

Step-by-step explanation: