Algebra

9.1 Square Roots

I will use the inverse of perfect squares to find approximate values of square roots.I will use square roots to evaluate radical expressions and solve equations.

Algebra

Objective

Algebra

9.1 Square Roots

Vocabulary• Square root - a number n such that if

multiplied by itself, it is equal to a perfect square

- n2 = x, where x is a perfect square

- the inverse of squaring a number

- all positive numbers have two square roots (1 positive, 1 negative)

Algebra

9.1 Square Roots

Vocabulary• Perfect square - a number that is a square of

an integer

- Examples: 1, 4, 9, 16, 25…

• Radicand - the number or expression inside a radical symbol

• Irrational Number - a number that cannot be written as the quotient of two integers (example: square roots)

• Radical Expression - an expression with a square root (or radical)

Algebra

9.1 Square RootsThink about the relationship between the area of a square and the length of one of its sides.

Taking the square root of a number is the inverse of squaring the number.

area = 36 square unitsside length = 36 = 6 units

62 = 36 36 = 6

Algebra

9.1 Square Roots

–49 is not the same as – 49. A negative number has no real square root.

Caution!

Algebra

9.1 Square Roots

A. 255 is a square root, since 5 • 5 = 25.–5 is also a square root, since –5 • –5 = 25.Rewrite as

12 is a square root, since 12 • 12 = 144.

–12 is also a square root, since –12 • –12 = 144.Rewrite as

Find the two square roots of each number.

B. 144

25 5

5

144 12

12

Algebra

9.1 Square Roots

A. 49

Guided PracticeFind the two square roots of each number.

B. 225

Algebra

9.1 Square Roots

132 = 169

The window is 13 inches wide.

Find the square root of 169 to find the width of the window. Use the positive square root; a negative length has no meaning.

Example 2: ApplicationA square window has an area of 169 square inches. How wide is the window?

So 169 = 13.

The area of a square is s2, where s is the length of a side.

Remember!

Algebra

9.1 Square Roots

Approximating a Square Root

• To approximate a square root

- choose one perfect square less than the number and one perfect square greater than the number

- take the square root of the perfect square of that is nearest to the original number

Algebra

9.1 Square Roots

Example 3: Approximating a Square Root

Find the square root of 78.

64 < 78 < 81 Identify the perfect squares closest to 78

78 is closer to 81 than 64.

Find the square root of 81

81 9

78 9

Algebra

9.1 Square Roots

Guided Practice

Find the square root of 135.

Algebra

9.1 Square Roots

Lesson Quiz

Find the two square roots of each number.

1. 81 2. 25009 50