Verified answer

Resposta:

[tex]\textsf{Leia abaixo}[/tex]

Explicação passo a passo:

[tex]\mathsf{\sqrt{A \pm \sqrt{B}} = \sqrt{\dfrac{A + C}{2}} \pm \sqrt{\dfrac{A - C}{2}}}[/tex]

[tex]\mathsf{\sqrt{\dfrac{30(3 + \sqrt{5})}{11}}}[/tex]

[tex]\mathsf{\sqrt{\dfrac{90 + 30\sqrt{5}}{11}}}[/tex]

[tex]\mathsf{\sqrt{\dfrac{90}{11} + \dfrac{30\sqrt{5}}{11}}}[/tex]

[tex]\mathsf{\sqrt{\dfrac{90}{11} + \sqrt{\dfrac{30^2.5}{11^2}}}}[/tex]

[tex]\mathsf{\sqrt{\dfrac{90}{11} + \sqrt{\dfrac{900.5}{121}}}}[/tex]

[tex]\mathsf{\sqrt{\dfrac{90}{11} + \sqrt{\dfrac{4.500}{121}}}}[/tex]

[tex]\mathsf{A = \dfrac{90}{11}}[/tex]

[tex]\mathsf{B = \dfrac{4.500}{121}}[/tex]

[tex]\mathsf{C = \sqrt{A^2 - B}}[/tex]

[tex]\mathsf{C = \sqrt{\dfrac{8.100}{121} - \dfrac{4.500}{121}}}[/tex]

[tex]\mathsf{C = \sqrt{\dfrac{3.600}{121}}}[/tex]

[tex]\mathsf{C = \dfrac{60}{11}}[/tex]

[tex]\mathsf{\sqrt{\dfrac{30(3 + \sqrt{5})}{11}} = \sqrt{\dfrac{90/11 + 60/11}{2}} + \sqrt{\dfrac{90/11 - 60/11}{2}}}[/tex]

[tex]\mathsf{\sqrt{\dfrac{30(3 + \sqrt{5})}{11}} = \sqrt{\dfrac{150/11}{2}} + \sqrt{\dfrac{30/11}{2}}}[/tex]

[tex]\mathsf{\sqrt{\dfrac{30(3 + \sqrt{5})}{11}} = \sqrt{\dfrac{150}{22}} + \sqrt{\dfrac{30}{22}}}[/tex]

[tex]\boxed{\boxed{\mathsf{\sqrt{\dfrac{30(3 + \sqrt{5})}{11}} = \sqrt{\dfrac{75}{11}} + \sqrt{\dfrac{15}{11}}}}}[/tex]