7 3 Square Roots and the Pythagorean Theorem

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7. 3 Square Roots and the Pythagorean Theorem Copyright © 2011 Pearson Education, Inc.

7. 3 Square Roots and the Pythagorean Theorem Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

The Square of a Number The square of a number is the number times

The Square of a Number The square of a number is the number times itself. The square of 6 is 36 because 62 = 36. The square of – 6 is also 36 because (– 6)2 = (– 6) = 36. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3 ed 2

Square Root of a Number The reverse process of squaring is finding a square

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

Square Root of a Number The square root, , of a positive number a

Square Root of a Number The square root, , of a positive number a is the positive number b whose square is a. In symbols, Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3 ed 4

Helpful Hint Remember that the radical sign is used to indicate the positive square

Helpful Hint Remember that the radical sign is used to indicate the positive square root of a nonnegative number. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3 ed 5

Perfect Squares Numbers like are called perfect squares because their square root is a

Perfect Squares Numbers like are called perfect squares because their square root is a whole number or a fraction. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3 ed 6

Approximating Square Roots A square root such as cannot be written as a whole

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. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3 ed 7

Right Triangles One important application of square roots has to do with right triangles.

Right Triangles 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. The legs of a right triangle are the other two sides. hypotenuse leg Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3 ed 8

Pythagorean Theorem If a and b are the lengths of the legs of a

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 a c b In other words, (leg)2 + (other leg)2 = (hypotenuse)2. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3 ed 9