Evaluating Algebraic Expressions

4-6 Squares and Square Roots

NS2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer.Also covered: AF2.2

California Standards

Evaluating Algebraic Expressions

4-6 Squares and Square Roots

The square root of a number is one of the two equal factors of that number.

Because the area of a square can be expressed using an exponent of 2, a number with an exponent of 2 is said to be squared. You read 32 as “three squared.”

3

3

Area = 32

Put the picture and red in notes.

Evaluating Algebraic Expressions

4-6 Squares and Square Roots

Positive real numbers have two square roots, one positive and one negative. The positive square root, or principle square root, is represented by . The negative square root is represented by – .

Notes

Evaluating Algebraic Expressions

4-6 Squares and Square Roots

You can write the square roots of 16 as ±4, which is read as “plus or minus four.”

Writing Math

Evaluating Algebraic Expressions

4-6 Squares and Square RootsAdditional Example: 1 Finding the Positive and Negative

Square Roots of a NumberFind the two square roots of each number.

7 is a square root, since 7 • 7 = 49.

–7 is also a square root, since –7 • (–7) = 49.49 = –7–

49 = 7

A. 49

The square roots of 49 are ±7.

Notes

Evaluating Algebraic Expressions

4-6 Squares and Square Roots

A. 25

Check It Out! Example 1

5 is a square root, since 5 • 5 = 25.

–5 is also a square root, since –5 • (–5) = 25.25 = –5–

25 = 5

Find the two square roots of each number.

The square roots of 25 are ±5.

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Evaluating Algebraic Expressions

4-6 Squares and 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.

Additional Example 2: Application

A square window has an area of 169 square inches. How wide is the window?

So 169 = 13.

Evaluating Algebraic Expressions

4-6 Squares and Square Roots

Find the square root of 16 to find the width of the table. Use the positive square root; a negative length has no meaning.

Check It Out! Example 2

A square shaped kitchen table has an area of 16 square feet. Will it fit through a van door that has a 5 foot wide opening?

So the table is 4 feet wide, which is less than 5 feet, so it will fit through the van door.

16 = 4

Evaluating Algebraic Expressions

4-6 Squares and Square RootsAdditional Example 3: Finding the Square Root of a

MonomialSimplify the expression.

A.

Write the monomial as a square.

Use the absolute-value symbol.= 12|c|

144c2

144c2 = (12c)2

Notes

Evaluating Algebraic Expressions

4-6 Squares and Square RootsAdditional Example 3: Finding the Square Root of a

Monomial

Simplify the expression.

C.

Write the monomial as a square.

10n2 is nonnegative for all values of n. The absolute-value symbol is not needed.

= 10n2

100n4

100n4 = (10n2)2

Notes

Evaluating Algebraic Expressions

4-6 Squares and Square RootsCheck It Out! Example 3

Simplify the expression.

A.

Write the monomial as a square.

Use the absolute-value symbol.= 11|r|

121r2

121r2 = (11r)2

B. p8

p8 = (p4)2

= |p4|

Write the monomial as a square: p8 = (p4)2

Use the absolute-value symbol.

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Evaluating Algebraic Expressions

4-6 Squares and Square RootsCheck It Out! Example 3

Simplify the expression.

C.

Write the monomial as a square.

9m2 is nonnegative for all values of m. The absolute-value symbol is not needed.

= 9m2

81m4

81m4 = (9m2)2

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