Question

rationalise the denominators of
$\frac{37}{7 + 3 \sqrt{2} }$
​

Answer 1

$\frac{7 + 2 \sqrt{3} }{7 - 2 \sqrt{3} }$

By rationlising the denominator,

$\frac{7 + 2 \sqrt{3} }{7 - 2 \sqrt{3} } \times \frac{7 + 2 \sqrt{3} }{7 + 2 \sqrt{3} }$

$\frac{( {7 + 2 \sqrt{3}) }^{2} }{ {7}^{2} - {(2 \sqrt{3)} }^{2} }$

$\frac{49 + 12 + 28 \sqrt{3} }{49 - 12}$

$\frac{61 + 28 \sqrt{3} }{37}$

Hope it helps......