Question

Two circular ponds at a botanical garden have the following radii. Pond A. 5√(164 ) meters

Answer 1

Answer:

The correct step will be $5(\sqrt{164})=5(\sqrt{4*41})$

Step-by-step explanation:

We have been given that pond A has a radius of $5\sqrt{(164)}$ meters and radius of Pond B is $\frac{(25\sqrt{200)}}{5}$ meters. Todd simplifies the radius of pond A and we are asked to find out error in Todd's steps.

Step 1: $5(\sqrt{100}+\sqrt{64})$

Since we know that $\sqrt{ab}=\sqrt{a\times b}=\sqrt{a} \times \sqrt{b}$. We can see that Todd has made error in his very first step by splitting $\sqrt{164}$ as $\sqrt{100+64}$.

The correct step will be,

$5(\sqrt{164})=5(\sqrt{4*41})$  

Therefore, the correct step 1 will be: $5(\sqrt{4*41})$.  

Now let us simplify our given radical expression.

$5(\sqrt{4*41})=5(\sqrt{4}*\sqrt{41})$  

$5\sqrt{4}*\sqrt{41}=5*2*\sqrt{41}$  

$5*2*\sqrt{41}=10*\sqrt{41}$  

Therefore, our given radical expression simplifies to $10*\sqrt{41}$ meters.