Question

I’m working on review questions to prepare for test and need help with this.

Answer 1

Step1: write out the expression

`\sqrt[]{125x}`

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

`125=25*5`

Step3: replace the product above with 125 in the expression

`\sqrt[]{125x}=\sqrt[]{25*5* x}`

Step4: simplify the last expression by applying the rational rule below

`\sqrt[]{a* b}=\sqrt[]{a}*\sqrt[]{b}`

Hence we have

`\sqrt[]{25*5* x}=\sqrt[]{25}*\sqrt[]{5}*\sqrt[]{x}`
`\sqrt[]{25}*\sqrt[]{5}*\sqrt[]{x}=5*\sqrt[]{5}*\sqrt[]{x}=5\sqrt[]{5x}`

Hence

`\sqrt[]{125x}=5\sqrt[]{5x}`

Therefore

A=5 and B=5x