The given expression is :
[tex]\sqrt[]{45}+\sqrt[]{125}[/tex]The expression for the square root is :
[tex]\sqrt[]{a^2}=a[/tex]In the given expression, simplify one by one :
[tex]\begin{gathered} \sqrt[]{45}\text{ } \\ \text{Factors of 45 = 5}\times3\times3 \\ \sqrt[]{45}\text{ =}\sqrt[]{5\times3\times3} \\ \sqrt[]{45}=\sqrt[]{5\times3^2} \\ \sqrt[]{45}=3\sqrt[]{5} \end{gathered}[/tex]Now :
[tex]\begin{gathered} \sqrt[]{125}\colon \\ \text{factors of 125 = 5}\times5\times5 \\ \sqrt[]{125}=\sqrt[]{5\times5\times5} \\ \sqrt[]{125}=\sqrt[]{5\times5^2} \\ \sqrt[]{125}=5\sqrt[]{5} \end{gathered}[/tex]Substitute the value in the expression and simplify :
[tex]\begin{gathered} \sqrt[]{45}+\sqrt[]{125}=3\sqrt[]{5}+5\sqrt[]{5} \\ \sqrt[]{45}+\sqrt[]{125}=(3+5)\sqrt[]{5} \\ \sqrt[]{45}+\sqrt[]{125}=8\sqrt[]{5} \end{gathered}[/tex]Answer : B)
[tex]8\sqrt[]{5}[/tex]
