1. Square Roots and the Pythagorean Theorem Section 6.4

2. The square of a number is the number times itself. The square of 6 is 36 because. 6 2 The square of - 6 is also 36 because.()()() -  --  66636 2  2 Martin-Gay, Prealgebra, 5ed

3. The reverse process of squaring is finding a square root. A square root of 36 is 6 because. 62 A square root of 36 is also 6 because 36 We use the symbol, called a radical sign, to indicate the positive square root. 16441642becauseandispositive. 2555255 2becauseandispositive. 3

4. Square Root of a Number Also, 0 = 0. a b,b,b,b,ifba2 9339 2because The square root,, of a positive number a is the positive number b whose square is a. In symbols, 4 Martin-Gay, Prealgebra, 5ed

5. Helpful Hint Remember that the radical sign is used to indicate the positive square root of a nonnegative number. 5 Martin-Gay, Prealgebra, 5ed

6. Numbers like are called perfect squares because their square root is a whole number or a fraction. 1 4 36 4 25 1,,,and 6 Martin-Gay, Prealgebra, 5ed

7. 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. 6 Approximating Square Roots 7 Martin-Gay, Prealgebra, 5ed

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

9. Pythagorean Theorem If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then abc 222 In other words, c a b (leg) 2 + (other leg) 2 = (hypotenuse) 2. 9 Martin-Gay, Prealgebra, 5ed