Question

Calculati :   a) √27/16+√75/144-√147/9
b) √882/81-√288/324+√50/4 
/ este fractie  27 supra 16
ajutorrr!!!

Answer 1

                
$a)\;\;\sqrt{ \frac{27}{16}} + \sqrt{ \frac{75}{144}} -\sqrt{ \frac{147}{9}}= \\ \\ = \sqrt{ \frac{9*3}{16}} + \sqrt{ \frac{25*3}{144}} -\sqrt{ \frac{49*3}{9}}= \\ \\ = \frac{3 \sqrt{3} }{4} + \frac{5\sqrt{3} }{12} - \frac{7\sqrt{3} }{3} = \;\;\;\;\;\text{(Numitorul comun este 12)} \\ \\ = \frac{3*3 \sqrt{3} }{12} + \frac{5\sqrt{3} }{12} - \frac{4*7\sqrt{3} }{12} = \\ \\ =\frac{9\sqrt{3}+ 5\sqrt{3}-28\sqrt{3}}{12}=\frac{ 14\sqrt{3}-28\sqrt{3}}{12}=\frac{ -14\sqrt{3}}{12}=\frac{ -7\sqrt{3}}{6}$
     
      
$b)\;\; \sqrt{ \frac{882}{81}}- \sqrt{ \frac{288}{324}}+\sqrt{ \frac{50}{4}}= \\ \\ =\sqrt{ \frac{441*2}{81}}- \sqrt{ \frac{144*2}{324}}+\sqrt{ \frac{25*2}{4}}= \\ \\ = \frac{21\sqrt{2} }{9}-\frac{12\sqrt{2} }{18} +\frac{5\sqrt{2} }{2}=\;\;\;\;\;\;\;\text{Numitorul comun este 18} \\ \\ =\frac{2*21\sqrt{2} }{18}-\frac{12\sqrt{2} }{18} +\frac{9*5\sqrt{2} }{18}= \\ \\ =\frac{42\sqrt{2} }{18}-\frac{12\sqrt{2} }{18} +\frac{45\sqrt{2} }{18}=\frac{42\sqrt{2}-12\sqrt{2}+ 45\sqrt{2}}{18} = \frac{75\sqrt{2} }{18}$ 

$= \frac{25\sqrt{2} }{6}$