Descompunem in factori primi numerele de sub radical pentru a ne fi mai usor la calcule
48 = 2⁴·3 => √48 = 4√3
32 = 2⁵ => √32 = 4√2
243 = 3⁵ => √243 = 9√3
[tex]\bf \sqrt{48} -\Big(\dfrac{16}{\sqrt{32}} -\dfrac{18}{\sqrt{243}}\Big)\cdot\sqrt{6} =[/tex]
[tex]\bf 4\sqrt{3} -\Big(\dfrac{16}{4\sqrt{2}} -\dfrac{18}{9\sqrt{3}}\Big)\cdot\sqrt{6} =[/tex]
[tex]\bf 4\sqrt{3} -\Big(\dfrac{\not16}{\not4\sqrt{2}} -\dfrac{\not18}{\not9\sqrt{3}}\Big)\cdot\sqrt{6} =[/tex]
[tex]\bf 4\sqrt{3} -\Big(\dfrac{4}{\sqrt{2}} -\dfrac{2}{\sqrt{3}}\Big)\cdot\sqrt{6} =[/tex]
[tex]\bf 4\sqrt{3} -\Big(\dfrac{4\cdot\sqrt{2} }{\sqrt{2}\cdot\sqrt{2} } -\dfrac{2\cdot\sqrt{3} }{\sqrt{3}\cdot\sqrt{3} }}\Big)\cdot\sqrt{6} =[/tex]
[tex]\bf 4\sqrt{3} -\Big(\dfrac{4\cdot\sqrt{2} }{2} -\dfrac{2\cdot\sqrt{3} }{3}}\Big)\cdot\sqrt{6} =[/tex]
[tex]\bf 4\sqrt{3} -\Big(\dfrac{\not4\cdot\sqrt{\not2}}{2} -\dfrac{2\cdot\sqrt{3} }{3}}\Big)\cdot\sqrt{6} =[/tex]
[tex]\bf 4\sqrt{3} -\Big(2\sqrt{2} -\dfrac{2\cdot\sqrt{3} }{3}}\Big)\cdot\sqrt{6} =[/tex]
[tex]\bf 4\sqrt{3} -\Big(2\sqrt{12} -\dfrac{2\cdot\sqrt{18} }{3}}\Big)=[/tex]
[tex]\bf 4\sqrt{3} -\Big(4\sqrt{3} -\dfrac{6\cdot\sqrt{2} }{3}}\Big)=[/tex]
[tex]\bf 4\sqrt{3} -\Big(4\sqrt{3} -\dfrac{\not6\cdot\sqrt{2} }{\not3}}\Big)=[/tex]
[tex]\bf 4\sqrt{3} -(4\sqrt{3} -2\sqrt{2})=[/tex]
[tex]\bf 4\sqrt{3} -4\sqrt{3} +2\sqrt{2}=[/tex]
[tex]\bf \not4\sqrt{3} -\not4\sqrt{3} +2\sqrt{2}=[/tex]
[tex]\boxed{\bf 2\sqrt{2}}[/tex]
PS: 1) Am incercat sa iti scriu toate calculele ca sa intelegi, daca ai intrebari imi scrii in comentarii
2) Am atasat si o fotografie in caz de telefonul tau nu citeste scrisul matematic
≈≈≈≈ Mult succes! ≈≈≈≈
