Question

3 - √5 ÷ 3 + 2 √5 rationalize

Answer 1

Answer:

Heya!

Your answer is here ☞☞☞

Step-by-step explanation:

$\frac{3 - \sqrt{5} }{3 + 2 \sqrt{5} }$

$= \frac{3 - \sqrt{5} }{3 + 2 \sqrt{5} } \times \frac{3 - 2 \sqrt{5} }{3 - 2 \sqrt{5} }$

$= \frac{(3 - \sqrt{5}) (3 - 2 \sqrt{5)} }{(3 + 2 \sqrt{5}) (3 - 2 \sqrt{5)} }$

$= \frac{9 - 6 \sqrt{5 } - 3 \sqrt{5} + 10 }{9 - 20}$

[use identity- (a+b)(a-b) = a²-b² for denominator.]

$= \frac{19 - 9 \sqrt{5} }{11}$

Hence, rationalised!