Question

Use the Pythagorean theorem to find x, in simplest radical form

Answer 1

Answer:

$x = 4 \sqrt{21}$

Answer 2

Answer:

$4\sqrt{21}$

Step-by-step explanation:

Pythagorean theorem is $a^{2} +b^{2} =c^{2}$.

Which in this case:

'c' is hypotenuse. (hypotenuse = 20)

'a' and 'b' are the other sides. (a = x, b = 8)

1. $a^{2} +b^{2}= c^{2}$
2. $x^{2} +8^{2} =20^{2}$
3. $x^{2} + 64 = 400$
4. $x^{2} = 336$

Now we should just take square root from the both sides.

and the answer will be $\sqrt{336}$ or $-\sqrt{336}$, but a side of a triangle can not be a negative number! so the answer will be $\sqrt{336}$.

As you see $\sqrt{336}$ is not the simplest radical.

We can write $\sqrt{336}$ as $\sqrt{16 * 21}$.

And from the laws of radical we can write $\sqrt{16*21}$ as $\sqrt{16} * \sqrt{21}$.

$\sqrt{16} * \sqrt{21} = \sqrt{16}\sqrt{21} = 4\sqrt{21}$

I hope it helps you. Please choose my answer as the brainliest.