Question

Rationalize the denominator of 3−2 √2 / 3+2 √2

Answer 1

Answer:

17 - 12√2

Step-by-step explanation:

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

{Using identity (a - b)² = a² + b² - 2ab}

{Using identity : (a + b)(a - b) = a² - b²}

$\frac{(3)^{2}+(2\sqrt{2})^{2} -2(3)(2\sqrt{2} ) }{(3)^{2} -(2\sqrt{2} )^{2} } \\\\\frac{9 + 8-12\sqrt{2} }{9-8} \\\\\frac{17-12\sqrt{2} }{1} \\\\17-12\sqrt{2}$