Question

rationalize 3+2√2/3-2√2​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The answer is $17+12\sqrt 2$

Step-by-step explanation:

Rationalize denominator  

$\dfrac{3+2\sqrt 2}{3-2\sqrt 2}\times \dfrac{3+2\sqrt 2}{3+2\sqrt 2}$

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

Using $(a+b)^2=a^2+2ab+b^2$ and $(a-b)(a+b)=a^2-b^2$