Respuesta :
Answer:
The correct step will be [tex]5(\sqrt{164})=5(\sqrt{4*41})[/tex]
Step-by-step explanation:
We have been given that pond A has a radius of [tex]5\sqrt{(164)}[/tex] meters and radius of Pond B is [tex]\frac{(25\sqrt{200)}}{5}[/tex] meters. Todd simplifies the radius of pond A and we are asked to find out error in Todd's steps.
Step 1: [tex]5(\sqrt{100}+\sqrt{64})[/tex]
Since we know that [tex]\sqrt{ab}=\sqrt{a\times b}=\sqrt{a} \times \sqrt{b}[/tex]. We can see that Todd has made error in his very first step by splitting [tex]\sqrt{164}[/tex] as [tex]\sqrt{100+64}[/tex].
The correct step will be,
[tex]5(\sqrt{164})=5(\sqrt{4*41})[/tex]
Therefore, the correct step 1 will be: [tex]5(\sqrt{4*41})[/tex].
Now let us simplify our given radical expression.
[tex]5(\sqrt{4*41})=5(\sqrt{4}*\sqrt{41})[/tex]
[tex]5\sqrt{4}*\sqrt{41}=5*2*\sqrt{41}[/tex]
[tex]5*2*\sqrt{41}=10*\sqrt{41}[/tex]
Therefore, our given radical expression simplifies to [tex]10*\sqrt{41}[/tex] meters.
