Question

What is the product?( square root 3x+ square root 5) (square root 15x+ 2 square root 30)

Answer 1

$(\sqrt{3x}+\sqrt5)\cdot(\sqrt{15x}+2\sqrt{30})$

$(\sqrt{3x})(\sqrt{15x})+(\sqrt{3x})(2\sqrt{30})+(\sqrt5)(\sqrt{15x})+(\sqrt5)(2\sqrt{30})$

$\sqrt{(3x)(15x)}+2\sqrt{(3x)(30)}+\sqrt{(5)(15x)}+2\sqrt{(5)(30)}$

$\sqrt{45x^2}+2\sqrt{90x}+\sqrt{75x}+2\sqrt{150}$

$\sqrt{9x^2\cdot5}+2\sqrt{9\cdot10x}+\sqrt{25\cdot3x}+2\sqrt{25\cdot6}$

$\sqrt{9x^2}\cdot\sqrt5+2\sqrt9\cdot\sqrt{10x}+\sqrt{25}\cdot\sqrt{3x}+2\sqrt{25}\cdot\sqrt{6}$

$3x\sqrt5+2\cdot3\sqrt{10x}+5\sqrt{3x}+2\cdot5\sqrt{6}$

$3x\sqrt5+6\sqrt{10}\sqrt{x}+5\sqrt{3}\sqrt{x}+10\sqrt{6}$

$3x\sqrt5+(6\sqrt{10}+5\sqrt{3})\sqrt{x}+10\sqrt{6}$

Answer 2

$(\sqrt{3x}+\sqrt5)\cdot(\sqrt{15x}+2\sqrt{30})\\\\=(\sqrt{3x})(\sqrt{15x})+(\sqrt{3x})(2\sqrt{30})+(\sqrt5)(\sqrt{15x})+(\sqrt5)(2\sqrt{30})\\\\=\sqrt{(3x)(15x)}+2\sqrt{(3x)(30)}+\sqrt{(5)(15x)}+2\sqrt{(5)(30)}\\\\=\sqrt{45x^2}+2\sqrt{90x}+\sqrt{75x}+2\sqrt{150}\\\\=\sqrt{9x^2\cdot5}+2\sqrt{9\cdot10x}+\sqrt{25\cdot3x}+2\sqrt{25\cdot6}\\\\=\sqrt{9x^2}\cdot\sqrt5+2\sqrt9\cdot\sqrt{10x}+\sqrt{25}\cdot\sqrt{3x}+2\sqrt{25}\cdot\sqrt6$
$=3x\sqrt5+2\cdot3\sqrt{10x}+5\sqrt{3x}+2\cdot5\sqrt6\\\\=3x\sqrt5+6\sqrt{10}+5\sqrt{3x}+10\sqrt6$