Question

Hey there Ms or Mr could you please help me out with this problem?just so you know, this is Pythagorean theorem & Simplifying Radicals My recent tutor said that this is the answer of course no I don't have any doubts I just want to know if this is correct.

Answer 1

When we have a radical, we can simplify it by the rule:

$\sqrt[]{ab}=\sqrt[]{a}\sqrt[]{b}$

So, we have to break down 500 into simpler radicals until we have a radical that can't be broken down. Let's simplify Root(500).

$\sqrt[]{500}=\sqrt[]{50}\sqrt[]{10}$

Now, we can break down Root(50) further.

$\begin{gathered} \sqrt[]{50}\sqrt[]{10} \\ =\sqrt[]{25}\sqrt[]{2}\sqrt[]{10} \end{gathered}$

Now, let's break down Root(10) also, thus we have:

$\begin{gathered} \sqrt[]{25}\sqrt[]{2}\sqrt[]{10} \\ =\sqrt[]{25}\sqrt[]{2}\sqrt[]{5}\sqrt[]{2} \end{gathered}$

We can see:

• Root(25) is 5

,

• Also Root(2)*Root(2) is 2 by using the rule:

$\sqrt[]{a}\sqrt[]{a}=a$

Thus, we finally have:

$\begin{gathered} \sqrt[]{25}\sqrt[]{2}\sqrt[]{5}\sqrt[]{2} \\ =5(2)\sqrt[]{5} \\ =10\sqrt[]{5} \end{gathered}$