Question

Rationalise the d
2
What is 2+ V3 as a
fraction with a
rational denominator?​

Answer 1

Answer:

Here is your answer:

Given ,

An number - \frac{1}{2+ \sqrt{3} }

2+

3

1

Objective:

To rationalize the denominator.

Solution,

To rationalize the denominator we must multiply and divide the number by the denominator's conjugate.

Conjugate of denominator is -- 2 + √3.

Then,

\frac{1}{2+ \sqrt{3} } \times \frac{2- \sqrt{3} }{2- \sqrt{3} } = \frac{2- \sqrt{3}}{(2+ \sqrt{3})(2- \sqrt{3}) }

2+

3

1

×

2−

3

2−

3

=

(2+

3

)(2−

3

)

2−

3

We know that, (a+b) ( a-b) = a² - b².

So, (2+√3)(2-√3) = 2² -(√3)² = 4 - 3 = 1.

Then,

⇒ \frac{2- \sqrt{3}}{(2+ \sqrt{3})(2- \sqrt{3}) } = \frac{2- \sqrt{3}}{1} = 2- \sqrt{3}

(2+

3

)(2−

3

)

2−

3

=

1

2−

3

=2−

3

Hence the denominator is rationalized.