Question

Rationalise 0%7D%20" id="TexFormula1" title="{ \frac{1 + \sqrt{3} }{ \sqrt{12} } } " alt="{ \frac{1 + \sqrt{3} }{ \sqrt{12} } } " align="absmiddle" class="latex-formula">
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Answer 1

Answer:

$\frac{2\sqrt{3} + 6}{12}$

Step-by-step explanation:

Simplify the denominator of $\frac{1 + \sqrt{3} }{\sqrt{12} }$ completely.

$=> \frac{1 + \sqrt{3} }{ \sqrt{(4 \times 3)} } = \frac{1 + \sqrt{3} }{\sqrt{4} \times \sqrt{3} } = \frac{1 + \sqrt{3} }{2\sqrt{3} }$

Now, to rationalise it you need to make the denominator rational.

• Multiply & divide $\frac{1 + \sqrt{3} }{2\sqrt{3} }$ by $2\sqrt{3}$.

$=> \frac{1 + \sqrt{3} }{2\sqrt{3} } \times \frac{2\sqrt{3} }{2\sqrt{3} }$

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

$=> \frac{2\sqrt{3} + 6 }{12}$

Answer 2

Answer:

Step-by-step explanation: