Question

Aduceti la o forma mai simpla expresia :
$\frac{ (\sqrt{7}-\sqrt{3} )^{2} +\sqrt{84} }{\sqrt{20}}$

Answer 1

[(√7-√3)²+√84]/√20=
=(7-2√21+3+2√21)/√20=
=10/√20=10√20/20=√20/2=
=2√5/2=√5

Answer 2

$\displaystyle \frac{( \sqrt{7}- \sqrt{3} )^2+ \sqrt{84} }{ \sqrt{20} } = \frac{ \sqrt{7^2}-2 \cdot \sqrt{7} \cdot \sqrt{3} + \sqrt{3^2}+2 \sqrt{21} }{2 \sqrt{5} } = \\ \\ = \frac{7-2 \sqrt{21}+3+2 \sqrt{21} }{2 \sqrt{5} } = \frac{7+3}{2 \sqrt{5} } = \frac{10}{2 \sqrt{5} }= \frac{5}{ \sqrt{5} } = \frac{5 \sqrt{5} }{5} = \sqrt{5}$