Question

2+root3/2-root3 rationalise the denominator

Answer 1

Answer:

7+4√3

Step-by-step explanation:

(2+√3/2-√3)×(2+√3/2+√3)

= (2+√3)²/2²-(√3)²

= 2²+2×2×√3+(√3)²/4-3

= 4+4√3+3/1

= 7+4√3

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Answer 2

The value of the expression after rationalizing is 7 + 4√3.

Step-by-step explanation:

The fraction is:

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

Rationalise the denominator as follows:

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

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

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

       $=\frac{4+3+4\sqrt{3}}{4-3}$

       $=7+4\sqrt{3}$

Thus, the value of the expression after rationalizing is 7 + 4√3.

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