Question

Rationalise the denominator of
1/2 + root3​

Answer 1

Step-by-step explanation:

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Answer 2

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 = 2− 3 =2− 3

Hence the denominator is rationalized.