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Square Roots and the Pythagorean Theorem

Learn how to calculate square roots and apply the Pythagorean Theorem in right triangles. Discover the significance of perfect squares and how to approximate square roots effectively.

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Square Roots and the Pythagorean Theorem

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  1. Square Roots and the Pythagorean Theorem 7.3

  2. The square of a number is the number times itself. The Square of a Number The square of 6 is 36 because 62 = 36. The square of –6 is also 36 because (–6)2 = (–6) (–6) = 36.

  3. Square Root of a Number The reverse process of squaring is finding a square root. A square root of 36 is 6 because 62 = 36. A square root of 36 is also –6 because (–6)2 = 36. Weuse the symbol , called aradical sign, to indicate the positive square root of a nonnegative number. because 42 = 16 and 4 is positive. because 52 = 25 and 5 is positive.

  4. Square Root of a Number The square root, , of a positive numberais the positive numberbwhosesquare isa. In symbols,

  5. Helpful Hint Remember that the radical sign is used to indicate the positive square root of a nonnegative number.

  6. Numbers like arecalled perfect squares because their square root is a whole number or a fraction. Perfect Squares

  7. Approximating Square Roots A square root such as cannot be written as a whole number or a fraction since 6 is not a perfect square. It can be approximated by estimating, by using a table, or by using a calculator.

  8. One important application of square roots has to do with right triangles. Right Triangles A right triangle is a triangle in which one of the angles is a right angle or measures 90º (degrees). Thehypotenuseof a right triangle is the side opposite the right angle. Thelegsof a right triangle are the other two sides. hypotenuse leg leg

  9. Pythagorean Theorem c a b If aand b are the lengths of the legs of aright triangle andcis the length of the hypotenuse, then In other words, (leg)2 + (other leg)2 = (hypotenuse)2.

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