Răspuns: Ai mai jos rezolvarea
Explicație pas cu pas:
Salutare!
[tex]\bf \sqrt{\dfrac{40}{18} } - \sqrt{\dfrac{54}{75}} =[/tex]
[tex]\bf \sqrt{\dfrac{40}{18}^{(2} } - \sqrt{\dfrac{54}{75}^{(3}} =[/tex]
Simplificam cu 2 primul radical si cu 3 al doilea radical
[tex]\bf \sqrt{\dfrac{20}{9}} - \sqrt{\dfrac{18}{25}} =[/tex]
[tex]\bf \sqrt{\dfrac{5\cdot2^{2}}{3^{2}}} - \sqrt{\dfrac{2\cdot3^{2}}{5^{2}}} =[/tex]
[tex]\bf \dfrac{2\sqrt{5}}{3} -\dfrac{3\sqrt{2}}{5}=[/tex]
[tex]\bf \dfrac{5\cdot2\sqrt{5}}{5\cdot3} -\dfrac{3\cdot3\sqrt{2}}{3\cdot5}=[/tex]
Aducem la același numitor
[tex]\boxed{\bf \dfrac{10\sqrt{5}-9\sqrt{2}}{15}}[/tex]
[tex]\bf \sqrt{\dfrac{40}{18} } = \sqrt{\dfrac{5\cdot 2^{3} }{2\cdot3^{2}}} =\dfrac{2\sqrt{10}}{3\sqrt{2}} =\dfrac{2\sqrt{10}}{3\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{2\sqrt{20}}{3\cdot 2} =\dfrac{\not2\sqrt{20}}{3\cdot \not2} =\dfrac{\sqrt{20}}{3}=\boxed{\bf \dfrac{2\sqrt{5}}{3}}[/tex]
[tex]\bf \sqrt{\dfrac{54}{75} } = \sqrt{\dfrac{2\cdot 3^{3} }{3\cdot5^{2}}} =\dfrac{3\sqrt{6}}{5\sqrt{3}} =\dfrac{3\sqrt{6}}{5\sqrt{3}}\cdot \dfrac{\sqrt{3}}{\sqrt{3}}=\dfrac{3\sqrt{18}}{5\cdot 3} =\dfrac{\not3\sqrt{18}}{5\cdot \not3} =\dfrac{\sqrt{18}}{5}=\boxed{\bf \dfrac{3\sqrt{2}}{5}}[/tex]
#copaceibrainly
