Question

So I’m doing this assignment and got stuck on this question can anyone help me

Answer 1

Step-by-step explanation:

The question involves dividing radicals

To resolve the question, we will follow the steps below

Step 1: Write the expression

`√(50x^3)/√(32x^2)`

Step 2: simplify the expression in parts and apply the laws

`\begin{gathered} √(50x^3)=√(25*2* x^2* x) \\ =√(25*2* x^2* x)=√(5^2*2* x^2* x)=√(5^2)*√(x^2)*√(2x) \end{gathered}`

Thus

`\begin{gathered} √(50x^3)=√(5^2)*√(x^2)*√(2x)=5* x*√(2x) \\ Therefore \\ √(50x^3)=5x√(2x) \end{gathered}`

For the second part

`√(32x^2)=√(16*2* x^2)`

simplifying further

`√(16*2* x^2)=√(16)*√(x^2)*√(2)`

Hence, we have

`√(16)*√(x^2)*√(2)=4* x*√(2)=4x√(2)`

Finally, we will combine the simplified terms, so that we will have

`√(50x^3)/√(32x^2)=5x√(2x)/4x√(2)`

Hence, we will have

`(5x√(2x))/(4x√(2))=(5)/(4)*(x)/(x)*(√(2))/(√(2))*(√(x))/(1)`

By canceling out the common parts, we will have the answer to be

`(5)/(4)√(x)`