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{30(3 + \sqrt{5})} = \sqrt{90 + 30\sqrt{5}}}[/tex]

[tex]\mathsf{\sqrt{90 + 30\sqrt{5}} = \sqrt{90 + \sqrt{30^2.5}}}[/tex]

[tex]\mathsf{\sqrt{90 + \sqrt{30^2.5}} = \sqrt{90 + \sqrt{900.5}}}[/tex]

[tex]\mathsf{\sqrt{90 + \sqrt{900.5}} = \sqrt{90 + \sqrt{4.500}}}[/tex]

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

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

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

[tex]\mathsf{C = \sqrt{(90)^2 - 4.500}}[/tex]

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

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

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

[tex]\mathsf{\sqrt{90 + \sqrt{4.500}} = \sqrt{\dfrac{90 + 60}{2}} + \sqrt{\dfrac{90 - 60}{2}}}[/tex]

[tex]\mathsf{\sqrt{90 + \sqrt{4.500}} = \sqrt{\dfrac{150}{2}} + \sqrt{\dfrac{30}{2}}}[/tex]

[tex]\mathsf{\sqrt{90 + \sqrt{4.500}} = \sqrt{75} + \sqrt{15}}[/tex]

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