7.3

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.