Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 7.3 Square Roots and the Pythagorean Theorem

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 22 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. The square of a number is the number times itself. The square of 6 is 36 because 6 2 = 36. The square of –6 is also 36 because The Square of a Number (–6) 2 = (–6) (–6) = 36.

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. A square root of 36 is 6 because A square root of 36 is 6 because 6 2 = 36. A square root of 36 is also 6 because ( A square root of 36 is also –6 because (–6) 2 = 36. Square Root of a Number We use the symbol, called a radical sign, to indicate the positive square root of a nonnegative number. because 4 2 = 16 and 4 is positive. because 5 2 = 25 and 5 is positive. The reverse process of squaring is finding a square root.

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Square Root of a Number The square root,, of a positive number a is the positive number b whose square is a. In symbols,

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Remember that the radical sign is used to indicate the positive square root of a nonnegative number. Helpful Hint

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Numbers like are called perfect squares because their square root is a whole number or a fraction. Perfect Squares

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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. Approximating Square Roots

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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 of a right triangle is the side opposite the right angle. The hypotenuse of a right triangle is the side opposite the right angle. hypotenuse leg The of a right triangle are the other two sides. The legs of a right triangle are the other two sides. Right Triangles

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 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 In other words, c a b (leg) 2 + (other leg) 2 = (hypotenuse) 2.