Question

$simplify - (\sqrt{5} + \sqrt{3} )( \sqrt{5} + \sqrt{3} ) \div 7 - 2 \sqrt{5 }$
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Answer 1

please see the attachment

Answer 2

Answer :-

⏩To Solve this equation we will use the BODMAS Rule .

In which

• B → Bracket

• O → Of

• D → Division

• M → Multiplication

• A → Addition

• S → Subtraction

◾ Simplification

$(\sqrt{5} + \sqrt{3})(\sqrt{5} + \sqrt{3}) \div 7 - 2\sqrt{5}$

$= (\sqrt{5} + \sqrt{3}) \dfrac{ (\sqrt{5} + \sqrt{3})}{7} - 2\sqrt{5}$

$= \dfrac{ (\sqrt{5} + \sqrt{3})^2}{7} - 2\sqrt{5}$

$= \dfrac{[(\sqrt{5})^2 + 2(\sqrt{5})(\sqrt{3}) + (\sqrt{3})^2]}{7} - 2\sqrt{5}$

$= \dfrac{ [5 + 2\sqrt{15} + 3 ]}{7} - 2\sqrt{5}$

$= \dfrac{[8 + 2\sqrt{15}]}{7} - 2\sqrt{5}$

$= \dfrac{[8 + 2\sqrt{15}] - 14\sqrt{5}}{7}$

$= \dfrac{ 8 + 2\sqrt{15} - 14\sqrt{5}}{7}$