Question

$7 + 3 \sqrt{5} \: 7 - 3 \sqrt{5}$
rationalize the denominator

Answer 1

heya!
$= > \frac{7 + 3 \sqrt{5} }{7 - 3 \sqrt{5} } \times \frac{7 + 3 \sqrt{5} }{7 + 3 \sqrt{5} } \\ = > \frac{( {7 + 3 \sqrt{5} })^{2} }{ {7}^{2} - {3 \sqrt{5} }^{2} } \\ = > \frac{49 + 45 + 42 \sqrt{5} }{49 - 45} \\ = > \frac{94 + 42 \sqrt{5} }{4}$
hope this helps you ☺

Answer 2

Heya!!!

Rationalize the Denominator

7 + 3√5 / 7 - 3√5
= 7 + 3√5 / 7 - 3√5 × 7 + 3√5 / 7 + √5
= 7² + 3√5² / 7² - 3√5²
= 49 + 45 / 49 - 45
= 94/4
= 23,5

May be usefull ^_^