Question

I’m doing a assignment and got stuck on this question if you could please help me that would be gladly appreciated

Answer 1

Given the expression:

`√(4x^2)\cdot√(20x^2)`

You can simplify each Radical as follows, in order to find an equivalent expression:

1. If you decompose the coefficient 4 and the coefficient 20 into their Prime Factors, you get:

`\begin{gathered} 4=2\cdot2=2^2 \\ \\ 20=2\cdot2\cdot5=2^2\cdot5 \end{gathered}`

Rewrite the Radicands:

`=√(2^2x^2)\cdot√(2^25^2x^2)`

2. Apply this Property for Radicals:

`\sqrt[n]{b^n}=b`

Then, you get:

`\begin{gathered} =2x\cdot2x\cdot√(5) \\ \\ =4x^2√(5) \end{gathered}`

Hence, the answer is: Option A.