find the length of the third side. if necessary, write in simplest radical form.\nanswer attempt 1 out of 2

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse $c = 2\sqrt{41}$ and one - side $a = 8$. The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$, so $b^{2}=c^{2}-a^{2}$.

Step2: Substitute values

$c^{2}=(2\sqrt{41})^{2}=4\times41 = 164$ and $a^{2}=8^{2}=64$. Then $b^{2}=164 - 64$.

Step3: Calculate $b^{2}$

$b^{2}=164−64 = 100$.

Step4: Find $b$

$b=\sqrt{100}=10$.

Answer:

10