Question

Which choice us equivalent to the product below when x >0?

Answer 1

We are given the following radical expression.

`\sqrt{(2)/(x)}\cdot\sqrt{(x^2)/(8)}`

Let us simplify the above expression.

Recall the product rule of radicals given by

`√(a)\cdot√(b)=√(a\cdot b)`

Apply the above rule to the given expression.

`\sqrt{(2)/(x)}\cdot\sqrt{(x^2)/(8)}\Rightarrow\sqrt{(2x^2)/(8x)}\Rightarrow\sqrt{(x)/(4)}`

Recall the quotient rule of radicals given by

`\sqrt{(a)/(b)}=(√(a))/(√(b))`

Apply the above rule to the given expression.

`\sqrt{(x)/(4)}\Rightarrow(√(x))/(√(4))\Rightarrow(√(x))/(2)`

Therefore, the simplified expression is

`(√(x))/(2)`

Option A is the correct answer.