Question

$\sqrt{2} * \sqrt{6} + \sqrt{5}* \sqrt{15}+ \sqrt{3}* \sqrt{27}- \sqrt{7}* \sqrt{21}$

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Answer 1

$\sqrt{2} \times \sqrt{6} + \sqrt{5} \times \sqrt{15} + \sqrt{3} \times \sqrt{27} - \sqrt{7} \times \sqrt{21} = \\ \\ \sqrt{12} + \sqrt{5} \times \sqrt{15} + \sqrt{3} \times 3 \sqrt{3} - \sqrt{7} \times \sqrt{21} = \\ \\ 2 \sqrt{3} + \sqrt{75} + \sqrt{3} \times 3 \sqrt{3} - \sqrt{7} \times \sqrt{21} = \\ \\ 2 \sqrt{3} + 5 \sqrt{3} + \sqrt{3} \times 3 \sqrt{3} + \sqrt{7} \times \sqrt{21} = \\ \\ 2 \sqrt{3} + 5 \sqrt{3} + 3 \sqrt{3 \times 3} + \sqrt{7} \times \sqrt{21} = \\ \\ 2 \sqrt{3} + 5 \sqrt{3} + 3 \sqrt{9} - \sqrt{7} \times \sqrt{21} = \\ \\ 2 \sqrt{3} + 5 \sqrt{3} + 3 \times 3 - \sqrt{7} \times \sqrt{21} = \\ \\ 2 \sqrt{3} + 5 \sqrt{3} + 9 - \sqrt{147} = \\ \\ 2 \sqrt{3} + 5 \sqrt{3} + 9 - 7 \sqrt{3} = \\ \\ (2 \sqrt{3} + 5 \sqrt{3} - 7 \sqrt{3}) + 9 = 9$

Answer 2

$\it \sqrt2\cdot\sqrt6 +\sqrt5\cdot\sqrt{15} +\sqrt3\cdot\sqrt{27} -\sqrt7\cdot\sqrt{21} = \sqrt2\cdot\sqrt2\cdot\sqrt3 + \\ \\ + \sqrt5\cdot\sqrt5\cdot\sqrt3+\sqrt{81} - \sqrt7\cdot\sqrt7\cdot\sqrt3=2\sqrt3 + 5\sqrt3+9-7\sqrt3 =9$