15.5 Chapter summary

• A square number (a perfect square) is the product of a number multiplied by itself.
• The number underneath the square root sign is called the radicand.
• A square root that cannot be simplified is called a surd.
• If we cannot remove the square root, then we say that the answer is in surd form.
• The theorem of Pythagoras is a rule that applies only to right-angled triangles.
• The side opposite the right angle of a right-angled triangle is called the hypotenuse.
• The hypotenuse is always the longest side of a right-angled triangle.
• If \(\triangle XYZ\) is a right-angled triangle with hypotenuse \(x\) and sides \(y\) and \(z\), then \(x^2 = y^2 + z^2\) (Pythagoras).
• If we know the lengths of all three sides of a triangle, we can use the theorem of Pythagoras to determine if a triangle is a right-angled triangle or not.