Question

examine the following triangle:
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using the pythagorean theorem, we can represent the side bc as ____, or __, which is ____.
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Explanation:

Step1: Recall Pythagorean theorem

For right triangle $\triangle ABC$, $BC^2 = AB^2 + AC^2$

Step2: Substitute given side lengths

$AB=2$, $AC=2$, so $BC^2 = 2^2 + 2^2$

Step3: Solve for BC (first form)

$BC = \sqrt{2^2 + 2^2}$

Step4: Simplify the radicand

$2^2 + 2^2 = 4 + 4 = 8$, so $BC = \sqrt{8}$

Step5: Simplify the radical

$\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}$

Answer:

$\sqrt{2^2 + 2^2}$, or $\sqrt{8}$, which is $2\sqrt{2}$