Simplify 7-3-57-3-5-3-53-5-

(7+3√( 5 ) )(7 3√( 5 ) ) (3+√( 5 ) )(3 √( 5 ) ) =7^2 (3√(5))^23^2 (√(5))^2=49 459 5=44=1 . ...

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Expansion of (a ± b ± c)²

Simplify 7+...

Question

Simplify $\frac{(7 + 3 \sqrt{5}) (7 - 3 \sqrt{5})}{(3 + \sqrt{5}) (3 - \sqrt{5})}$ .

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Solution

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

Simplify :

(i) $\frac{3 \sqrt{2} - 2 \sqrt{3}}{3 \sqrt{2} + 2 \sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}$

(ii) $\frac{7 + 3 \sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3 \sqrt{5}}{3 - \sqrt{5}}$

{(\frac{5}{8})}^{- 3} \times {(\frac{4}{5})}^{- 3} \div {(\frac{4}{5})}^{3}

5 \sqrt{5} \times 5^{3} \div 5^{- 3 / 2}

{(\frac{4}{5})}^{- 5} \times {(\frac{5^{3}}{4^{3}})}^{- 3}

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