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Chapter summary

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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.