Question

Să se transforme radicali compuși
$\sqrt{3 - \sqrt{5} }$
$\sqrt{9 + 4 \sqrt{5} }$
$\sqrt{3 + \sqrt{5} }$
$\sqrt{9 - 4 \sqrt{5} }$

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Answer 1

Avem formula:

$C=\sqrt{A^2-B} \\\\\sqrt{\frac{A+C}{2} } \pm\sqrt{\frac{A-C}{2} }$

A=3

B=5

C=2

$\sqrt{3-\sqrt{5} } =\sqrt{\frac{5}{2} } -\sqrt{\frac{1}{2} }$

A=9

B=80

C=1

$\sqrt{9+4\sqrt{5} } =\sqrt{5} +2$

A=3

B=5

C=2

$\sqrt{3+\sqrt{5} } =\sqrt{\frac{5}{2} }+\sqrt{\frac{1}{2} }$

A=9

B=80

C=1

$\sqrt{9-4\sqrt{5} } =\sqrt{5} -2$

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