Given a triangle ABC, in which AB = √5, CB = √3, AC = √2. is it a right-angled triangle?

Since the condition contains the lengths of all sides of the triangle, assume that the triangle is right-angled and define the sides of the triangle.

In a right-angled triangle, the hypotenuse is the largest of the sides, then AB = √5 is the hypotenuse, CB = √3 and AC = √2 are the legs.

Then, by the Pythagorean theorem, equality must be satisfied.

AB ^ 2 = CB ^ 2 + AC ^ 2.

(√5) ^ 2 = (√3) ^ 2 + (√2) ^ 2.

5 = 3 + 2.

5 = 5.

Answer: The ABC triangle is rectangular.