Question

pls ! urgent !!!!!!!!!​

Answer 1

$\Big(2\sqrt{5} -\sqrt{2}\Big)\cdot \Big(\sqrt{5}+\sqrt{2}\Big)\cdot \Big(2\sqrt{5}-3\sqrt{2} \Big)=\\\\=\Big(2\sqrt{5} \cdot \sqrt{5} +2\sqrt{5} \cdot \sqrt{2}-\sqrt{2}\cdot \sqrt{5} -\sqrt{2} \cdot \sqrt{2}\Big)\cdot\Big(2\sqrt{5}-3\sqrt{2}\Big)=\\\\=\Big(2 \cdot 5 +2\sqrt{10}-\sqrt{10} -\sqrt{4} \Big)\cdot \Big(2\sqrt{5} -3\sqrt{2}\Big)=\\\\=\Big(10+\sqrt{10}-2\Big)\cdot \Big(2\sqrt{5}-3\sqrt{2}\Big) =\Big(8+\sqrt{10} \Big)\cdot (2\sqrt{5} -3\sqrt{2}\Big)=$

$=8 \cdot 2\sqrt{5} -8 \cdot 3\sqrt{2} +\sqrt{10}\cdot 2\sqrt{5} -\sqrt{10} \cdot 3\sqrt{2} =\\\\=16\sqrt{5} -24\sqrt{2} +2\sqrt{50} -3\sqrt{20} =16\sqrt{5} -24\sqrt{2} +2 \cdot 5\sqrt{2} -3 \cdot 2\sqrt{5} =\\\\=16\sqrt{5} -24\sqrt{2} +10\sqrt{2} -6\sqrt{5} =\boxed{10\sqrt{5} -14\sqrt{2}}$

Answer 2

Explicație pas cu pas:

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

$= (10 + 2 \sqrt{10} - \sqrt{10} - 2)(2 \sqrt{5} - 3 \sqrt{2})$

$= (8 + \sqrt{10})(2 \sqrt{5} - 3 \sqrt{2})$

$= 16 \sqrt{5} - 24 \sqrt{2} + 10 \sqrt{2} - 6 \sqrt{5}$

$= 10 \sqrt{5} - 14 \sqrt{2}$