Question

Rationalize the denominator of 3+2root7/3-2root7

Answer 1

Answer:

$= \dfrac{3 + 2\sqrt{7} }{3 - 2 \sqrt{7} }$

multiply and divide with 3 + √7

$= \frac{3 + 2 \sqrt{7} }{3 - 2 \sqrt{7} } \times \frac{ 3 + 2\sqrt{7} }{ 3 + 2\sqrt{7} } \\ \\ = \dfrac{(3 + 2\sqrt{7})( 3 + 2\sqrt{7} )}{(3 - 2 \sqrt{7}) (3 + 2\sqrt{7}) }$

Using

(a + b)(a + b) = (a + b)² = a² + 2ab + b²

(a + b)(a - b) = a² - b²

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

$= \dfrac{ {3}^{2} + 12 \sqrt{7} + 14}{9 - 14}$

$= \: - \dfrac{25 + 2 \sqrt{7} }{5}$

Hence rationalised

Concepts used:

=⟩ Surds

=⟩ Rationalised