Answer:
[tex]\boxed{x=1}[/tex]
Step-by-step explanation:
[tex](x+3)^{\frac{3}{2}}-8=0[/tex]
[tex](x+3)^{\frac{3}{2}}=8[/tex]
[tex](x+3)^{\frac{3}{2} \cdot 2}=8^2[/tex]
[tex](x+3)^{3}=64[/tex]
[tex]x+3=\sqrt[3]{64}[/tex]
[tex]x+3=\sqrt[3]{4^3}[/tex]
[tex]x+3=4[/tex]
[tex]x=1[/tex]
