Question

If A= [5+2root2]/[3-2root2] is rationalized simplified form is

Answer 1

Answer:

39√2/5

Step-by-step explanation:

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

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

$\boxed {\sf{ {a}^{2} - {b}^{2} = (a + b) \: (a - b)}}$

$\bold{ = \frac{15 + 10 \sqrt{2} + 6 \sqrt{2} + 8 }{ {3}^{2} - {2 \sqrt{2} }^{2} }}$

$\bold{ = \frac{23 + 16 \sqrt{2} }{9 - 4}}$

$\bold{ = \frac{39 \sqrt{2} }{5}}$

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