SOLUTION
Step1: write out the expression
[tex]\sqrt[]{125x}[/tex]
we have to write this expression in its simplest form to identify the value of A and B
Step2: Identify the perfect square and write has a product
[tex]125=25\times5[/tex]
Step3: replace the product above with 125 in the expression
[tex]\sqrt[]{125x}=\sqrt[]{25\times5\times x}[/tex]
Step4: simplify the last expression by applying the rational rule below
[tex]\sqrt[]{a\times b}=\sqrt[]{a}\times\sqrt[]{b}[/tex]
Hence we have
[tex]\sqrt[]{25\times5\times x}=\sqrt[]{25}\times\sqrt[]{5}\times\sqrt[]{x}[/tex][tex]\sqrt[]{25}\times\sqrt[]{5}\times\sqrt[]{x}=5\times\sqrt[]{5}\times\sqrt[]{x}=5\sqrt[]{5x}[/tex]
Hence
[tex]\sqrt[]{125x}=5\sqrt[]{5x}[/tex]
Therefore
A=5 and B=5x
