Question

2 root 3 + 6 / root 3

Rationalise

Answer 1

Answer:

$2 \sqrt{3} + 6 \div \sqrt{3} = 2 \times 3 + 6 \div \sqrt{3} = 12 \div \sqrt{3} = 12 \times \sqrt{3} \div \sqrt{3} \times \sqrt{3} = 12 \sqrt{3} \div 3 = 4 \sqrt{3}$

Answer 2

Step-by-step explanation:

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

$= \frac{2 \sqrt{3} + 6 }{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \: \: \: \: (rationalise \: the \: denominator)$

$= \frac{ \sqrt{3}(2 \sqrt{3} + 6)}{ \sqrt{3} \times \sqrt{3} }$

$= \frac{2 \sqrt{3} \times \sqrt{3} + \sqrt{6} \times \sqrt{3} }{3}$

$= \frac{2 \times 3 + \sqrt{18} }{3}$

$= \frac{6 + \sqrt{2 \times 3 \times 3} }{3}$

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

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

$= 2 + \sqrt{2}$