Solve $c=\sqrt{3^2+4^2}$

Step-by-step solution

1. Step 1 · Pythagorean theorem
   $$a^2+b^2=c^2$$

   Valid because the triangle contains a right angle.

2. Step 2 · Substitute the legs
   $$9+16=25$$

   Square each leg and add.

3. Step 3 · Take the positive root
   $$c=\sqrt{25}=5$$

   Lengths are positive, so the negative root is discarded.