Question

Aduceți la o formă mai simplă :
$5 \sqrt{2} + 2 \sqrt{ 32} - \sqrt{ 98} =$
$( \sqrt{5} - \sqrt{3} ) ^{2} =$
$(4 \sqrt{3} + \sqrt{27} ) \times \sqrt{3} =$
$\sqrt{5} - \sqrt{21} \times \sqrt{5} + \sqrt{21} =$
Ajutați-mă va rog frumos..​

Answer 1

$5 \sqrt{2} + 2 \sqrt{32} - \sqrt{98} = \\ = 5 \sqrt{2} + {(2 \sqrt{32} )}^{2} - 7\sqrt{2} \\ = 5 \sqrt{2} + 4 \times 32 - 7 \sqrt{2} \\ = - 2 \sqrt{2} + 128 \\ = - 2 \sqrt{2} + \sqrt{128} \\ = - 2 \sqrt{2} + 8 \sqrt{2} \\ = 6 \sqrt{2} \\ \\ \\ {( \sqrt{5} - \sqrt{3})}^{2} = 5 - 3 = 2 \\ \\ \\ (4 \sqrt{3} + \sqrt{27} ) \times \sqrt{3} = \\ = (4 \sqrt{3} + 3 \sqrt{3} ) \times \sqrt{3} \\ = 7 \sqrt{3} \times \sqrt{3} \\ = 7 \times 3 \\ = 21 \\ \\ \\ \sqrt{5} - \sqrt{21} \times \sqrt{5} + \sqrt{21} = \\ = \sqrt{5} - \sqrt{105} + \sqrt{21}$