Question

Cual es el resultado de estos problemas :
1)√50-√18/4+√72/25
2)√5a²- √80a²+ √20a²
3)2√180+3/5√125+√5

30 PUNTOS !!! 

Answer 1

$1) \sqrt{50} - \sqrt{ \frac{18}{4}} + \sqrt{ \frac{72}{25}} = \\ \\ factorizamos \ cada \ raiz \\ \\ \sqrt{50}= \sqrt{5^{2}*2} = 5 \sqrt{2} \\ \\ \sqrt{ \frac{18}{4}}= \sqrt{ \frac{3^{2}*2}{2^{2}}} = \frac{3}{2} \sqrt{2} \\ \\ \sqrt{ \frac{72}{25}}= \sqrt{ \frac{6^{2}*2}{5^{2}}}= \frac{6}{5} \sqrt{2} \\ \\ entonces \\ \\ 5 \sqrt{2} - \frac{3}{2} \sqrt{2} + \frac{6}{5} \sqrt{2} =$

$5 \sqrt{2} - \frac{3}{2} \sqrt{2} + \frac{6}{5} \sqrt{2} = \\ \\ \sqrt{2} (5 - \frac{3}{2} + \frac{6}{5}) = \\ \\ \sqrt{2} ( \frac{50}{10} - \frac{15}{10} + \frac{12}{10}) = \boxed{\frac{47}{10} \sqrt{2}}$


$2) \sqrt{5a^{2} }- \sqrt{80a^{2}} + \sqrt{20a^{2}}= \\ \\ a\sqrt{5 }-a \sqrt{2^{4}* 5} + a \sqrt{2 ^{2}*5}= \\ \\ a\sqrt{5 }-a * 4 \sqrt{ 5} + a*2 \sqrt{5}= \\ \\ a\sqrt{5 }-4a \sqrt{ 5} + 2a \sqrt{5}= \\ \\ \boxed {-a \sqrt{5}}$


$3)2 \sqrt{180}+ \frac{3}{5} \sqrt{125}+ \sqrt{5} = \\ \\ 2 \sqrt{2^{2}*3^{2}*5}+ \frac{3}{5} \sqrt{5 ^{2}*5}+ \sqrt{5} = \\ \\ 2*2*3 \sqrt{5}+ \frac{3}{5}*5 \sqrt{5}+ \sqrt{5} = \\ \\ 12 \sqrt{5}+ 3\sqrt{5}+ \sqrt{5} = \\ \\ \boxed{16 \sqrt{5}}$

Espero que te sirva, salu2!!!!